ChemWiki - User contributions [en]

Rep:Mod:cma209

2013-02-08T16:48:36Z

Cma209: /* IRC Path of Endo & Exo transition states */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

===== IRC Path of Endo & Exo transition states =====

IRC analysis was done for both Endo and Exo transition states to follow the reaction pathway from reactions to products.

{| class="wikitable" border="1"
|+ Bond Lengths
! IRC (Exo TS) !! IRC (Endo TS)
|-
| style="text-align: center;|[[File:Irc exo.gif|250px]]
| style="text-align: center;|[[File:Irc endo.gif|250px]]
|-
| style="text-align: center;|[[File:Irc path exo.png|250px]]
| style="text-align: center;|[[File:Irc path1.png|250px]]
|}

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== MO Analysis of endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Nodal analysis.png|250px]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

The Secondary orbital overlap effect is defined as the positive overlap of a non reactive frame in the frontier molecular orbitals of a pericyclic reaction. The effect is crucial in the determination of regiochemistry of the Diels-Alder cycloaddition as evident by thermochemical, bond lengths, and MO analysis done above. They all point to the same conclusion that the endo transition state is the more stabilised one compared to the exo transition state. The overlap effect between the non reactive -(C=O)-O-(C=O)- fragment and the conjugated diene lowers the transition state energy and gives rise to a preferential formation of a kinetic product that resembles the endo transition state.

In these calculations of Diels Alder transition states, some factors that also affect the regiochemistry of the final cycloaddition product have been neglected. Bulky substituents in the dienophile component will usually favour the formation of the exo product over the more sterically crowded endo product. Also, if the Diels Alder reaction is subjected to thermodynamic conditions (i.e. high temperatures over a long period of reaction), the thermodynamic exo product may be preferred over the kinetic product as it is the more stable product.

Although the secondary orbital overlap effect can often effectively control the regiochemistry of the Diels Alder reaction, it bears no sterochemical control at all. Stereochemistry of the Diels Alder cycloaddition is determined instead by the stereochemistry of the starting materials and Diels Alder reaction is typically suprafacial.

File:Irc path exo.png

2013-02-08T16:46:54Z

Cma209:

File:Irc path1.png

2013-02-08T16:46:53Z

Cma209:

File:Irc endo.gif

2013-02-08T16:46:53Z

Cma209:

File:Irc exo.gif

2013-02-08T16:46:52Z

Cma209:

Rep:Mod:cma209

2013-02-08T16:43:32Z

Cma209: /* Optimising the Endo transition state */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

===== IRC Path of Endo & Exo transition states =====

IRC analysis was done for both Endo and Exo transition states to follow the reaction pathway from reactions to products.

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== MO Analysis of endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Nodal analysis.png|250px]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

The Secondary orbital overlap effect is defined as the positive overlap of a non reactive frame in the frontier molecular orbitals of a pericyclic reaction. The effect is crucial in the determination of regiochemistry of the Diels-Alder cycloaddition as evident by thermochemical, bond lengths, and MO analysis done above. They all point to the same conclusion that the endo transition state is the more stabilised one compared to the exo transition state. The overlap effect between the non reactive -(C=O)-O-(C=O)- fragment and the conjugated diene lowers the transition state energy and gives rise to a preferential formation of a kinetic product that resembles the endo transition state.

In these calculations of Diels Alder transition states, some factors that also affect the regiochemistry of the final cycloaddition product have been neglected. Bulky substituents in the dienophile component will usually favour the formation of the exo product over the more sterically crowded endo product. Also, if the Diels Alder reaction is subjected to thermodynamic conditions (i.e. high temperatures over a long period of reaction), the thermodynamic exo product may be preferred over the kinetic product as it is the more stable product.

Although the secondary orbital overlap effect can often effectively control the regiochemistry of the Diels Alder reaction, it bears no sterochemical control at all. Stereochemistry of the Diels Alder cycloaddition is determined instead by the stereochemistry of the starting materials and Diels Alder reaction is typically suprafacial.

Rep:Mod:cma209

2013-02-08T16:38:10Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== MO Analysis of endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Nodal analysis.png|250px]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

The Secondary orbital overlap effect is defined as the positive overlap of a non reactive frame in the frontier molecular orbitals of a pericyclic reaction. The effect is crucial in the determination of regiochemistry of the Diels-Alder cycloaddition as evident by thermochemical, bond lengths, and MO analysis done above. They all point to the same conclusion that the endo transition state is the more stabilised one compared to the exo transition state. The overlap effect between the non reactive -(C=O)-O-(C=O)- fragment and the conjugated diene lowers the transition state energy and gives rise to a preferential formation of a kinetic product that resembles the endo transition state.

In these calculations of Diels Alder transition states, some factors that also affect the regiochemistry of the final cycloaddition product have been neglected. Bulky substituents in the dienophile component will usually favour the formation of the exo product over the more sterically crowded endo product. Also, if the Diels Alder reaction is subjected to thermodynamic conditions (i.e. high temperatures over a long period of reaction), the thermodynamic exo product may be preferred over the kinetic product as it is the more stable product.

Although the secondary orbital overlap effect can often effectively control the regiochemistry of the Diels Alder reaction, it bears no sterochemical control at all. Stereochemistry of the Diels Alder cycloaddition is determined instead by the stereochemistry of the starting materials and Diels Alder reaction is typically suprafacial.

Rep:Mod:cma209

2013-02-08T16:33:15Z

Cma209: /* Conclusion */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Nodal analysis.png|250px]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

The Secondary orbital overlap effect is defined as the positive overlap of a non reactive frame in the frontier molecular orbitals of a pericyclic reaction. The effect is crucial in the determination of regiochemistry of the Diels-Alder cycloaddition as evident by thermochemical, bond lengths, and MO analysis done above. They all point to the same conclusion that the endo transition state is the more stabilised one compared to the exo transition state. The overlap effect between the non reactive -(C=O)-O-(C=O)- fragment and the conjugated diene lowers the transition state energy and gives rise to a preferential formation of a kinetic product that resembles the endo transition state.

In these calculations of Diels Alder transition states, some factors that also affect the regiochemistry of the final cycloaddition product have been neglected. Bulky substituents in the dienophile component will usually favour the formation of the exo product over the more sterically crowded endo product. Also, if the Diels Alder reaction is subjected to thermodynamic conditions (i.e. high temperatures over a long period of reaction), the thermodynamic exo product may be preferred over the kinetic product as it is the more stable product.

Although the secondary orbital overlap effect can often effectively control the regiochemistry of the Diels Alder reaction, it bears no sterochemical control at all. Stereochemistry of the Diels Alder cycloaddition is determined instead by the stereochemistry of the starting materials and Diels Alder reaction is typically suprafacial.

Rep:Mod:cma209

2013-02-08T16:23:06Z

Cma209: /* Conclusion */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Nodal analysis.png|250px]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

The Secondary orbital overlap effect is defined as the positive overlap of a non reactive frame in the frontier molecular orbitals of a pericyclic reaction. The effect is crucial in the determination of regiochemistry of the Diels-Alder cycloaddition as evident by thermochemical, bond lengths, and MO analysis done above. They all point to the same conclusion that the endo transition state is the more stabilised one compared to the exo transition state. The overlap effect between the non reactive -(C=O)-O-(C=O)- fragment and the conjugated diene lowers the transition state energy and gives rise to a preferential formation of a kinetic product that resembles the endo transition state.

In these calculations of Diels Alder transition states, some factors that also affect the regiochemistry of the final cycloaddition product have been neglected. Steric effects for one determines

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T16:19:31Z

Cma209: /* Conclusion */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Nodal analysis.png|250px]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

The Secondary orbital overlap effect is defined as the positive overlap of a non reactive frame in the frontier molecular orbitals of a pericyclic reaction. The effect is crucial in the determination of regiochemistry of the Diels-Alder cycloaddition as evident by thermochemical, bond lengths, and MO analysis done above. They all point to the same conclusion that the endo transition state is the more stabilised one compared to the exo transition state. The overlap effect between the non reactive

What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T16:14:07Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Nodal analysis.png|250px]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

File:Nodal analysis.png

2013-02-08T16:13:37Z

Cma209:

Rep:Mod:cma209

2013-02-08T16:12:25Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Iii OCO MO chemdraw WSM.png|250px]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T16:12:09Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker (minimal) than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

[[File:Iii OCO MO chemdraw WSM.png]]

When comparing the interaction between -(C=O)-O-(C=O)- fragment and the remainder of the system, we can observe nodal lobes present around each O atom for both the exo and endo HOMOs. The size of the nodal area between the fragment and the remainder of the system also indicates the degree of stabilization of the endo orientation compared to the exo one. For the endo transition state, there is a much larger central bonding interaction in the middle (between the diene and dienophile) and a small nodal area. This is indicative of the attractive interaction between the carbons in the O=C-O-C=O fragment and the non bond-forming carbons of the diene component. In contrast, the nodal area between -(C=O)-O-(C=O)- fragment and the remainder of the exo system is large as conjugated diene faces away from the -(C=O)-O-(C=O)- and interaction is impossible.

=== Conclusion ===

What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T15:42:06Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

As observed from the HOMO of the exo TS, the nodal

Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T15:38:12Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|200px]]
| style="text-align: center;|[[File:Lumo exo.png|200px]]
| style="text-align: center;|[[File:Homo endo.png|200px]]
| style="text-align: center;|[[File:Lumo endo.png|200px]]
|}

Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T15:35:47Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

{| class="wikitable" border="1"
|+
! HOMO (EXO) !! LUMO (EXO) !! HOMO (ENDO) !! LUMO (ENDO)
|-
| style="text-align: center;|[[File:Homo exo.png|250px]]
| style="text-align: center;|[[File:Lumo exo.png|250px]]
| style="text-align: center;|[[File:Homo endo.png|250px]]
| style="text-align: center;|[[File:Lumo endo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T15:30:42Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that in the endo form, the electronegative -(C=O)-O-(C=O)- fragment is right underneath the conguated diene component and can can be stabilised by pi-pi interactions (secondary orbital overlap effect) between the groups. There is also secondary orbital overlap effect in the exo form but is a lot less effective overlap is observed. In the exo form, the C-C (unconjugated) fragment is now spatially accessible by the -(C=O)-O-(C=O)- fragment for interaction. However, sp-p interaction is much weaker than pi-pi interaction in the endo form. The HOMO/LUMO comparison diagram below illustrates the secondary orbital overlap effects that enhances the stability of endo form over the corresponding exo form.

Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

File:Endo ts3.png

2013-02-08T15:21:13Z

Cma209: uploaded a new version of "File:Endo ts3.png"

Rep:Mod:cma209

2013-02-08T15:18:09Z

Cma209: /* Structure difference between endo and exo form */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that the electronegative oxygen groups are

Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T15:14:38Z

Cma209: /* Energy Difference */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form).

{| class="wikitable" border="1"
|+ Bond Lengths
! EXO TS !! ENDO TS
|-
| style="text-align: center;|[[File:Exo ts3.png|250px]]
| style="text-align: center;|[[File:Endo ts3.png|250px]]
|}

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that the electronegative oxygen groups are

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T15:12:42Z

Cma209: /* Cyclohexa-1,3-diene with maleic anhydride */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

==== Comparison of Exo/Endo Transition States ====

===== Energy Difference =====

The energy of Exo TS is -0.05041979 au and the energy of Endo TS is -0.05150480 au. Energy difference is therefore 0.00109 au, equivalent to 0.684 kcal/mol. Thus Endo TS is 0.684 kcal/mol more stable than the Endo TS. With addition of zero-point energies, Exo TS has an energy of 0.134881 au while Endo TS has an energy of 0.133494 au. Energy difference is 0.872 kcal/mol, still indicative that endo TS is the more stable one.

The bond lengths of the endo and exo transition states are also indication of stability of the transition states. The bond forming carbon atoms are slightly closer together at the endo transition state, compared to that at the exo transition state. The presence of secondary orbital overlap effect can also be observed from the bond distance between the non-bonded carbonyl carbons of maleic anhydride and carbons of C=C bond (in endo form) or C-C bond (in exo form)

===== Structure difference between endo and exo form =====

The main structure difference between the endo and exo form is that the electronegative oxygen groups are

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

File:Lumo exo.png

2013-02-08T14:57:53Z

Cma209:

File:Lumo endo.png

2013-02-08T14:57:53Z

Cma209:

File:Homo exo.png

2013-02-08T14:57:52Z

Cma209:

File:Homo endo.png

2013-02-08T14:57:52Z

Cma209:

File:Exo ts3.png

2013-02-08T14:57:51Z

Cma209:

File:Endo ts3.png

2013-02-08T14:57:51Z

Cma209:

Rep:Mod:cma209

2013-02-08T14:33:00Z

Cma209:

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

Sum of electronic and zero-point Energies= 0.133494
Sum of electronic and thermal Energies= 0.143683
Sum of electronic and thermal Enthalpies= 0.144628
Sum of electronic and thermal Free Energies= 0.097350

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T14:32:12Z

Cma209: /* Optimising the Endo transition state */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

[[File:Endo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

[[File:Endo ts vib.gif|250px]]

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T14:30:55Z

Cma209: /* Optimising the Exo transition state */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

Sum of electronic and zero-point Energies= 0.134881
Sum of electronic and thermal Energies= 0.144882
Sum of electronic and thermal Enthalpies= 0.145827
Sum of electronic and thermal Free Energies= 0.099117

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T14:30:05Z

Cma209: /* Optimising the Exo transition state */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T14:29:51Z

Cma209: /* Optimising the Endo transition state */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.#

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

Rep:Mod:cma209

2013-02-08T14:29:27Z

Cma209: /* Optimising the Endo transition state */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.#

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Endo TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05150480
|-
| Gradient || 0.00000684 au
|-
| Dipole Moment || 6.1660 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:ENDO TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000533 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-7.799391D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -806.3619 -1.8701 -1.4257 -0.5415 -0.0104 0.4321
Low frequencies --- 1.1389 62.4149 111.7337
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. Frequency analysis shows an imaginary frequency obtained at -806.3619 cm-1, indicative of a transition state. Visualisation of the transition state can prove the

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.

File:Endo ts vib.gif

2013-02-08T14:26:27Z

Cma209:

File:Endo ts.png

2013-02-08T14:26:26Z

Cma209: uploaded a new version of "File:Endo ts.png"

File:ENDO TS.LOG

2013-02-08T14:26:26Z

Cma209: uploaded a new version of "File:ENDO TS.LOG"

Rep:Mod:cma209

2013-02-08T14:19:50Z

Cma209: /* Optimisation of ethylene+cis-butadiene transition state */

== Week 1 ==

=== Cope Rearrangement of 1,5-hexadiene -- Reactants/Products Optimisation ===

==== 1,5-hexadiene (anti2) ====

[[File:Anti2.png|200px]]

===== Constructing the molecule =====

Gaussview was used to draw 1,5-hexadiene. A ethyl fragment was first added to the Molecule screen, and rotated till it resembles a Newman projection.

[[File:Anti2 newman.png|200px]]

Subsequently, to ensure an anti linkage, 2 vinyl fragments were used to replace the hydrogens on opposite ends. The dihedral angles are modified such that the C=C bonds are oriented such that they resemble approximately the low energy conformers shown in [[Mod:phys3#Appendix 1|Appendix 1]].

===== Optimisation =====

Then, the molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69253523
|-
| Gradient || 0.00002918 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 3 sec
|}

Symmetry: Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000124 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000892 0.001800 YES
RMS Displacement 0.000306 0.001200 YES
Predicted change in Energy=-7.599488D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5526 -DE/DX = 0.0001 !
! R2 R(1,3) 1.0848 -DE/DX = 0.0 !
! R3 R(1,4) 1.0856 -DE/DX = 0.0 !
! R4 R(1,7) 1.5089 -DE/DX = 0.0 !
! R5 R(2,5) 1.0856 -DE/DX = 0.0 !
! R6 R(2,6) 1.0848 -DE/DX = 0.0 !
! R7 R(2,12) 1.5089 -DE/DX = 0.0 !
! R8 R(7,8) 1.3161 -DE/DX = 0.0 !
! R9 R(7,9) 1.0769 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0747 -DE/DX = 0.0 !
! R12 R(12,13) 1.3161 -DE/DX = 0.0 !
! R13 R(12,14) 1.0769 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0747 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.4077 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.3463 -DE/DX = 0.0 !
! A3 A(2,1,7) 111.3501 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.7097 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.9642 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.9762 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.3463 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.4077 -DE/DX = 0.0 !
! A9 A(1,2,12) 111.3501 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.7097 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.9762 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.9642 -DE/DX = 0.0 !
! A13 A(1,7,8) 124.8132 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.5057 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6732 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8655 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8234 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.311 -DE/DX = 0.0 !
! A19 A(2,12,13) 124.8132 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.5057 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.6732 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8655 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8234 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.311 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 62.8308 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -58.2382 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -62.8308 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.9311 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.9311 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 58.2382 -DE/DX = 0.0 !
! D9 D(7,1,2,12) -180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 114.6529 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -64.3192 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -6.7853 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 174.2427 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -125.2363 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 55.7917 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -114.6529 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 64.3192 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 125.2363 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -55.7917 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 6.7853 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -174.2427 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.113 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 1.0564 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.1808 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0114 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.113 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -1.0564 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.1808 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 180.0114 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

The anti2 conformer has dihedral angles of approximately 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69253523 au) with anti2 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

Link:{{DOI|10042/22959}}

====1,5-hexadiene (Gauche structures)====

Other 1,5-hexadiene structures were similarly constructed from an ethyl fragment and 2 vinyl fragments. However, as with Newman projection below, the vinyl groups are no longer anti-periplanar but are gauche to one another. Different gauche conformers can be obtained from rotation of vinyl groups on both ends and low energy conformers from [[Mod:phys3#Appendix 1|Appendix 1]] were used as reference. the gauche4 and gauche3 structures were constructed and optimised.

=====Optimising 1-5-hexadiene (gauche4) =====

[[File:Gauche4.png|200px]][[File:Gauche4 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche4) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69153032
|-
| Gradient || 0.00001866 au
|-
| Dipole Moment || 0.1281 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 1 min 47 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001569 0.001800 YES
RMS Displacement 0.000413 0.001200 YES
Predicted change in Energy=-4.919439D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5553 -DE/DX = 0.0 !
! R2 R(1,3) 1.0852 -DE/DX = 0.0 !
! R3 R(1,4) 1.0846 -DE/DX = 0.0 !
! R4 R(1,12) 1.5099 -DE/DX = 0.0 !
! R5 R(2,5) 1.0852 -DE/DX = 0.0 !
! R6 R(2,6) 1.0846 -DE/DX = 0.0 !
! R7 R(2,7) 1.5099 -DE/DX = 0.0 !
! R8 R(7,8) 1.3164 -DE/DX = 0.0 !
! R9 R(7,9) 1.0757 -DE/DX = 0.0 !
! R10 R(8,10) 1.0734 -DE/DX = 0.0 !
! R11 R(8,11) 1.0748 -DE/DX = 0.0 !
! R12 R(12,13) 1.3164 -DE/DX = 0.0 !
! R13 R(12,14) 1.0757 -DE/DX = 0.0 !
! R14 R(13,15) 1.0734 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.2989 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.7737 -DE/DX = 0.0 !
! A3 A(2,1,12) 112.3874 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.9502 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.8658 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.4551 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.2989 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.7737 -DE/DX = 0.0 !
! A9 A(1,2,7) 112.3874 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.9502 -DE/DX = 0.0 !
! A11 A(5,2,7) 109.8658 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.4551 -DE/DX = 0.0 !
! A13 A(2,7,8) 124.4248 -DE/DX = 0.0 !
! A14 A(2,7,9) 116.0435 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.5293 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8674 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.8481 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.2841 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.4248 -DE/DX = 0.0 !
! A20 A(1,12,14) 116.0435 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.5293 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8674 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.8481 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2841 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 179.4349 -DE/DX = 0.0 !
! D2 D(3,1,2,6) -63.4838 -DE/DX = 0.0 !
! D3 D(3,1,2,7) 57.8803 -DE/DX = 0.0 !
! D4 D(4,1,2,5) -63.4838 -DE/DX = 0.0 !
! D5 D(4,1,2,6) 53.5975 -DE/DX = 0.0 !
! D6 D(4,1,2,7) 174.9616 -DE/DX = 0.0 !
! D7 D(12,1,2,5) 57.8803 -DE/DX = 0.0 !
! D8 D(12,1,2,6) 174.9616 -DE/DX = 0.0 !
! D9 D(12,1,2,7) -63.6743 -DE/DX = 0.0 !
! D10 D(2,1,12,13) -109.4464 -DE/DX = 0.0 !
! D11 D(2,1,12,14) 69.9908 -DE/DX = 0.0 !
! D12 D(3,1,12,13) 129.8974 -DE/DX = 0.0 !
! D13 D(3,1,12,14) -50.6654 -DE/DX = 0.0 !
! D14 D(4,1,12,13) 11.5273 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -169.0355 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -109.4464 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 69.9908 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 129.8974 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -50.6654 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 11.5273 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -169.0355 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.2055 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -1.036 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.2134 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.5451 -DE/DX = 0.0 !
! D26 D(1,12,13,15) 179.2055 -DE/DX = 0.0 !
! D27 D(1,12,13,16) -1.036 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.2134 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.5451 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22960}}

Symmetry Point Group: C2

The gauche4 conformer has dihedral angles of approximately ±109.5o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69153032 au) with gauche4 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

=====Optimising 1,5-hexadiene (gauche3) =====

[[File:Gauche3.png|200px]][[File:Gauch3 newman.png|200px]]

The molecule is cleaned and optimised via the following set-up and submission to HPC portal:

Optimisation Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (gauche3) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.00001556 au
|-
| Dipole Moment || 0.3409 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 1 min 28 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001380 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.609980D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5531 -DE/DX = 0.0 !
! R2 R(1,3) 1.0872 -DE/DX = 0.0 !
! R3 R(1,4) 1.0844 -DE/DX = 0.0 !
! R4 R(1,12) 1.5085 -DE/DX = 0.0 !
! R5 R(2,5) 1.0836 -DE/DX = 0.0 !
! R6 R(2,6) 1.0867 -DE/DX = 0.0 !
! R7 R(2,7) 1.5093 -DE/DX = 0.0 !
! R8 R(7,8) 1.3165 -DE/DX = 0.0 !
! R9 R(7,9) 1.0772 -DE/DX = 0.0 !
! R10 R(8,10) 1.0735 -DE/DX = 0.0 !
! R11 R(8,11) 1.0745 -DE/DX = 0.0 !
! R12 R(12,13) 1.3163 -DE/DX = 0.0 !
! R13 R(12,14) 1.0751 -DE/DX = 0.0 !
! R14 R(13,15) 1.0735 -DE/DX = 0.0 !
! R15 R(13,16) 1.0748 -DE/DX = 0.0 !
! A1 A(2,1,3) 108.6453 -DE/DX = 0.0 !
! A2 A(2,1,4) 109.3261 -DE/DX = 0.0 !
! A3 A(2,1,12) 111.775 -DE/DX = 0.0 !
! A4 A(3,1,4) 107.5309 -DE/DX = 0.0 !
! A5 A(3,1,12) 109.7234 -DE/DX = 0.0 !
! A6 A(4,1,12) 109.738 -DE/DX = 0.0 !
! A7 A(1,2,5) 109.1939 -DE/DX = 0.0 !
! A8 A(1,2,6) 108.4634 -DE/DX = 0.0 !
! A9 A(1,2,7) 111.8673 -DE/DX = 0.0 !
! A10 A(5,2,6) 107.8754 -DE/DX = 0.0 !
! A11 A(5,2,7) 110.2758 -DE/DX = 0.0 !
! A12 A(6,2,7) 109.064 -DE/DX = 0.0 !
! A13 A(2,7,8) 125.0243 -DE/DX = 0.0 !
! A14 A(2,7,9) 115.3003 -DE/DX = 0.0 !
! A15 A(8,7,9) 119.6747 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8438 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.7797 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.3762 -DE/DX = 0.0 !
! A19 A(1,12,13) 124.5298 -DE/DX = 0.0 !
! A20 A(1,12,14) 115.5492 -DE/DX = 0.0 !
! A21 A(13,12,14) 119.9143 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.7758 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.9606 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.2635 -DE/DX = 0.0 !
! D1 D(3,1,2,5) -175.9065 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 66.7784 -DE/DX = 0.0 !
! D3 D(3,1,2,7) -53.556 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 67.0142 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -50.3009 -DE/DX = 0.0 !
! D6 D(4,1,2,7) -170.6353 -DE/DX = 0.0 !
! D7 D(12,1,2,5) -54.6864 -DE/DX = 0.0 !
! D8 D(12,1,2,6) -172.0015 -DE/DX = 0.0 !
! D9 D(12,1,2,7) 67.6641 -DE/DX = 0.0 !
! D10 D(2,1,12,13) 120.8781 -DE/DX = 0.0 !
! D11 D(2,1,12,14) -58.1813 -DE/DX = 0.0 !
! D12 D(3,1,12,13) -118.5285 -DE/DX = 0.0 !
! D13 D(3,1,12,14) 62.4122 -DE/DX = 0.0 !
! D14 D(4,1,12,13) -0.5848 -DE/DX = 0.0 !
! D15 D(4,1,12,14) -179.6442 -DE/DX = 0.0 !
! D16 D(1,2,7,8) -117.2338 -DE/DX = 0.0 !
! D17 D(1,2,7,9) 62.4576 -DE/DX = 0.0 !
! D18 D(5,2,7,8) 4.4965 -DE/DX = 0.0 !
! D19 D(5,2,7,9) -175.812 -DE/DX = 0.0 !
! D20 D(6,2,7,8) 122.783 -DE/DX = 0.0 !
! D21 D(6,2,7,9) -57.5256 -DE/DX = 0.0 !
! D22 D(2,7,8,10) 179.8706 -DE/DX = 0.0 !
! D23 D(2,7,8,11) -0.3243 -DE/DX = 0.0 !
! D24 D(9,7,8,10) 0.1917 -DE/DX = 0.0 !
! D25 D(9,7,8,11) -180.0032 -DE/DX = 0.0 !
! D26 D(1,12,13,15) -179.4375 -DE/DX = 0.0 !
! D27 D(1,12,13,16) 0.6328 -DE/DX = 0.0 !
! D28 D(14,12,13,15) -0.4166 -DE/DX = 0.0 !
! D29 D(14,12,13,16) 179.6537 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

Link:{{DOI|10042/22953}}

Symmetry Point Group: C1
The gauche4 conformer has dihedral angles of approximately ±120o on both C1-C2-C3-C4 and C3-C4-C5-C6, where C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 are the terminal C=C groups. Comparision of energy (-231.69266120 au) with gauche3 conformer in [[Mod:phys3#Appendix 1|Appendix 1]] indicates that the correct conformer has been obtained.

==== Optimising 1,5-hexadiene (anti2) at higher basis set ====

A lower and more accurate minimum could be obtained by subjecting the molecule to a higher basis set. This process however takes longer to complete. The log file of optimised (basis set: 3-21g) 1,5-hexadiene (anti2) was copied into a new molecule window and was further optimised with a better basis set (6-31Gd).

Method: DFT/B3LYP
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001331 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 29 sec
|}

<pre>

Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000223 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-1.591799D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.5481 -DE/DX = 0.0 !
! R2 R(1,3) 1.098 -DE/DX = 0.0 !
! R3 R(1,4) 1.0997 -DE/DX = 0.0 !
! R4 R(1,7) 1.5042 -DE/DX = 0.0 !
! R5 R(2,5) 1.0997 -DE/DX = 0.0 !
! R6 R(2,6) 1.098 -DE/DX = 0.0 !
! R7 R(2,12) 1.5042 -DE/DX = 0.0 !
! R8 R(7,8) 1.3335 -DE/DX = 0.0 !
! R9 R(7,9) 1.0919 -DE/DX = 0.0 !
! R10 R(8,10) 1.0868 -DE/DX = 0.0 !
! R11 R(8,11) 1.0885 -DE/DX = 0.0 !
! R12 R(12,13) 1.3335 -DE/DX = 0.0 !
! R13 R(12,14) 1.0919 -DE/DX = 0.0 !
! R14 R(13,15) 1.0868 -DE/DX = 0.0 !
! R15 R(13,16) 1.0885 -DE/DX = 0.0 !
! A1 A(2,1,3) 109.6058 -DE/DX = 0.0 !
! A2 A(2,1,4) 108.1899 -DE/DX = 0.0 !
! A3 A(2,1,7) 112.672 -DE/DX = 0.0 !
! A4 A(3,1,4) 106.6601 -DE/DX = 0.0 !
! A5 A(3,1,7) 109.742 -DE/DX = 0.0 !
! A6 A(4,1,7) 109.7814 -DE/DX = 0.0 !
! A7 A(1,2,5) 108.1899 -DE/DX = 0.0 !
! A8 A(1,2,6) 109.6058 -DE/DX = 0.0 !
! A9 A(1,2,12) 112.672 -DE/DX = 0.0 !
! A10 A(5,2,6) 106.6601 -DE/DX = 0.0 !
! A11 A(5,2,12) 109.7814 -DE/DX = 0.0 !
! A12 A(6,2,12) 109.742 -DE/DX = 0.0 !
! A13 A(1,7,8) 125.2867 -DE/DX = 0.0 !
! A14 A(1,7,9) 115.7271 -DE/DX = 0.0 !
! A15 A(8,7,9) 118.9815 -DE/DX = 0.0 !
! A16 A(7,8,10) 121.8701 -DE/DX = 0.0 !
! A17 A(7,8,11) 121.6516 -DE/DX = 0.0 !
! A18 A(10,8,11) 116.4778 -DE/DX = 0.0 !
! A19 A(2,12,13) 125.2867 -DE/DX = 0.0 !
! A20 A(2,12,14) 115.7271 -DE/DX = 0.0 !
! A21 A(13,12,14) 118.9815 -DE/DX = 0.0 !
! A22 A(12,13,15) 121.8701 -DE/DX = 0.0 !
! A23 A(12,13,16) 121.6516 -DE/DX = 0.0 !
! A24 A(15,13,16) 116.4778 -DE/DX = 0.0 !
! D1 D(3,1,2,5) 64.0627 -DE/DX = 0.0 !
! D2 D(3,1,2,6) 180.0 -DE/DX = 0.0 !
! D3 D(3,1,2,12) -57.4932 -DE/DX = 0.0 !
! D4 D(4,1,2,5) 180.0 -DE/DX = 0.0 !
! D5 D(4,1,2,6) -64.0627 -DE/DX = 0.0 !
! D6 D(4,1,2,12) 58.4441 -DE/DX = 0.0 !
! D7 D(7,1,2,5) -58.4441 -DE/DX = 0.0 !
! D8 D(7,1,2,6) 57.4932 -DE/DX = 0.0 !
! D9 D(7,1,2,12) 180.0 -DE/DX = 0.0 !
! D10 D(2,1,7,8) 118.5279 -DE/DX = 0.0 !
! D11 D(2,1,7,9) -60.6757 -DE/DX = 0.0 !
! D12 D(3,1,7,8) -3.9023 -DE/DX = 0.0 !
! D13 D(3,1,7,9) 176.8941 -DE/DX = 0.0 !
! D14 D(4,1,7,8) -120.8239 -DE/DX = 0.0 !
! D15 D(4,1,7,9) 59.9725 -DE/DX = 0.0 !
! D16 D(1,2,12,13) -118.5279 -DE/DX = 0.0 !
! D17 D(1,2,12,14) 60.6757 -DE/DX = 0.0 !
! D18 D(5,2,12,13) 120.8239 -DE/DX = 0.0 !
! D19 D(5,2,12,14) -59.9725 -DE/DX = 0.0 !
! D20 D(6,2,12,13) 3.9023 -DE/DX = 0.0 !
! D21 D(6,2,12,14) -176.8941 -DE/DX = 0.0 !
! D22 D(1,7,8,10) -179.5641 -DE/DX = 0.0 !
! D23 D(1,7,8,11) 0.7139 -DE/DX = 0.0 !
! D24 D(9,7,8,10) -0.3842 -DE/DX = 0.0 !
! D25 D(9,7,8,11) 179.8938 -DE/DX = 0.0 !
! D26 D(2,12,13,15) 179.5641 -DE/DX = 0.0 !
! D27 D(2,12,13,16) -0.7139 -DE/DX = 0.0 !
! D28 D(14,12,13,15) 0.3842 -DE/DX = 0.0 !
! D29 D(14,12,13,16) -179.8938 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved. The minimum energy obtained using this basis set is lower (-234.61170274 au) compared to the minimum energy obtained using the lower basis set (-231.69253523 au). This indicates that the higher basis set has indeed provided us with a lower and more accurate minimum energy.

Link:{{DOI|10042/22962}}

The optimised conformer has dihedral angles (±118o) that is closer to 120o on both C1-C2-C3-C4 and C3-C4-C5-C6, as compared to that of the lower basis set optimisation (±115o). As before, C3 and C4 are the middle ethyl fragment while C1, C2 and C5, C6 refer to the terminal C=C groups. This also indicates that a better optimisation has been obtained using the higher basis set, as dihedral angles obtained are closer to the ideal theoretical dihedral angle of 120o that gives the minimum energy.

====Frequency calculation of 1,5-hexadiene (anti2) ====

A frequency calculation is crucial in the determination of whether or not a minimum has been reached. The frequency analysis is essential the second derivative of the PES of a reaction, and if all frequencies obtained are positive, a minimum is reached. A transition state is reached if one of the frequencies obtained is negative. Optimisation is incomplete or failed if more than one negative frequencies have been obtained. Also, frequency analysis provides information with IR-active or Raman-active vibrations could be detected and compared with experimental values.

Using 6-31G(d) optimised 1,4-hexadiene (anti2), a frequency calculation is set-up:

Method: DFT/B3LYP 
Basis Set:6-31Gd

{| class="wikitable" border="1"
|+
! 1,5-hexadiene (Anti2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.61170274
|-
| Gradient || 0.00001338 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 3 min 27 sec
|}

Symmetry: Ci

Link:{{DOI|10042/22964}}

=====Low frequencies Table=====

Low frequencies --- -18.8017 -11.7161 -0.0012 -0.0010 -0.0006 1.7416
Low frequencies --- 72.7187 80.1386 120.0141

The first vibration listed is 72.7187cm-1 which is real. There are no imaginary frequencies obtained. All frequencies obtained are real nad positive, therefore, a minimum has been reached.

=====IR Spectrum=====

The vibrations could be visualised via an IR Spectrum, though only IR-active vibrations can be observed. For a vibrational mode to be considered IR-active, it must undergo a change in a dipole moment. The rule only requires a change in dipole moment, thus can be a temporary dipole.

[[File:IR Spectrum (anti hexadiene).png|550px]]

{| class="wikitable" border="1"
|+
! Frequency of Vibration / cm-1 !! Infrared absorption intensity
|-
| 72.72 || 0.0185
|-
| 80.14 || 0.1187
|-
| 120.01 || 0
|-
| 219.76 || 0.1592
|-
| 348.85 || 0
|-
| 394.29 || 0
|-
| 461.68 || 2.8940
|-
| 625.67 || 0
|-
| 669.40 || 20.0234
|-
| 787.80 || 4.0256
|-
| 938.19 || 8.9020
|-
| 938.65 || 0
|-
| 940.12 || 64.7206
|-
| 941.79 || 0
|-
| 1002.03 || 0
|-
| 1033.75 || 0
|-
| 1035.98 || 19.7410
|-
| 1042.72 || 0
|-
| 1067.94 || 9.5813
|-
| 1203.21 || 0
|-
| 1250.95 || 0.5904
|-
| 1288.84 || 6.4705
|-
| 1323.03 || 0
|-
| 1339.07 || 0
|-
| 1343.14 || 1.3918
|-
| 1384.10 || 0
|-
| 1473.71 || 0
|-
| 1476.22 || 1.5099
|-
| 1508.56 || 0
|-
| 1523.21 || 5.6212
|-
| 1730.95 || 0
|-
| 1734.24 || 18.1433
|-
| 3021.69 || 0
|-
| 3031.33 || 53.6390
|-
| 3060.30 || 0
|-
| 3080.32 || 35.8433
|-
| 3135.92 || 0
|-
| 3136.98 || 56.0529
|-
| 3155.47 || 14.7174
|-
| 3155.73 || 0
|-
| 3233.89 || 0
|-
| 3233.92 || 45.4813
|}

As seen in the table above, a lot of vibrational modes have an infrared absorption intensity of zero and also, does not show up in the IR spectrum above. This is due the high symmetry (Ci)of the anti2 1,5-hexadiene leading to many vibrations that do not generate a dipole moment, thus are IR-inactive.

====Thermochemistry====

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

=== Optimizing the "Chair" and "Boat" Transition Structures of Cope Rearrangement===

Optimising the transition state structures are a much more complex process as compared to optimising the reactants and products. This is because in order for calculation to be accurate, Gaussian needs to know which direction of curvature is the negative one, and it can do so by computing a force constant matrix also known as the Hessian. This calculation method however requires the guess transition state structure to be close enough to the actual transition state structure. If not, the curvature obtained at that particular surface may be significantly different from that of the actual surface. For 1,5-hexadiene, optimising the transition state involves forming and breaking of a bond and can go via a chair transition state or a boat transition state. By optimising to a chair and boat transition state and comparing the relative energies, we can determine which is the transition state stucture that is lowest energy transition state. The Cope rearrangement is a kinetic process, thus the reaction will proceed via the lowest transition state.

==== Optimizing Allyl Fragment CH2CHCH2 ====

The first step of optimising the chair transition state would be optimisation of a half of the hexadiene - an allyl fragment.

[[File:Allyl fragment.png|200px]]

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Allyl Fragment CH2CHCH2 !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || UHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -115.82304009
|-
| Gradient || 0.00003730 au
|-
| Dipole Moment || 0.0292 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 32 sec
|}

Link: [[File:Allyl Fragment.log]]

Symmetry : C2V

<pre>

Item Value Threshold Converged?
Maximum Force 0.000089 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000148 0.001200 YES
Predicted change in Energy=-2.381053D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.0757 -DE/DX = -0.0001 !
! R2 R(2,3) 1.3885 -DE/DX = 0.0001 !
! R3 R(2,6) 1.3885 -DE/DX = 0.0001 !
! R4 R(3,4) 1.0722 -DE/DX = 0.0 !
! R5 R(3,5) 1.074 -DE/DX = 0.0 !
! R6 R(6,7) 1.074 -DE/DX = 0.0 !
! R7 R(6,8) 1.0722 -DE/DX = 0.0 !
! A1 A(1,2,3) 117.8547 -DE/DX = 0.0 !
! A2 A(1,2,6) 117.855 -DE/DX = 0.0 !
! A3 A(3,2,6) 124.2903 -DE/DX = 0.0 !
! A4 A(2,3,4) 121.4189 -DE/DX = 0.0 !
! A5 A(2,3,5) 121.1232 -DE/DX = 0.0 !
! A6 A(4,3,5) 117.4579 -DE/DX = 0.0 !
! A7 A(2,6,7) 121.1214 -DE/DX = 0.0 !
! A8 A(2,6,8) 121.4209 -DE/DX = 0.0 !
! A9 A(7,6,8) 117.4578 -DE/DX = 0.0 !
! D1 D(1,2,3,4) 0.0 -DE/DX = 0.0 !
! D2 D(1,2,3,5) -180.0 -DE/DX = 0.0 !
! D3 D(6,2,3,4) 180.0 -DE/DX = 0.0 !
! D4 D(6,2,3,5) 0.0 -DE/DX = 0.0 !
! D5 D(1,2,6,7) 180.0 -DE/DX = 0.0 !
! D6 D(1,2,6,8) 0.0 -DE/DX = 0.0 !
! D7 D(3,2,6,7) 0.0 -DE/DX = 0.0 !
! D8 D(3,2,6,8) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

The optimisation was successful as convergence to a minimum was achieved.

==== Optimizing and Frequency Analysis of Chair TS ====

Following the optimisation of an allyl fragment, the optimized fragment was copied twice into a separate molecule window and oriented to resemble the chair transition state in [[Mod:phys3#Appendix 2|Appendix 2]].

[[File:Chair ts 321.png|200px]]

Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Transition State !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932239
|-
| Gradient || 0.00003282 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || Ci
|-
| Calculation Time Taken || 0 min 13 sec
|}

Link:[[File:CHAIR TS GUESS1.LOG]]

Energy of optimised compound = -231.61932239 au
Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000042 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001299 0.001800 YES
RMS Displacement 0.000147 0.001200 YES
Predicted change in Energy=-8.939592D-08
Optimization completed.
-- Stationary point found.

Low frequencies --- -817.8876 -4.9327 -2.1079 -0.0006 -0.0004 0.0002
Low frequencies --- 4.8688 209.5842 396.0987

</pre>

[[File:Chair negative vibration.gif|250px]]

The optimisation was successful as convergence to a transition state was achieved. One of the low frequencies obtained is an imaginary frequency at -817.8876 cm-1, which is indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Redundant Coordinate Method of Optimisation ====

Another method of optimisation of transition state involves the use of a redundant coordinate parameter. This allows us to freeze the reactive centres and hence minimize the rest of the molecule first. Subsequently, the reactive centres are unfrozen and optimized with the rest of the molecule already at the minimum. This often gives a more accurate determination of the transition state optimum.

The same guess structure used in the previous part was used as a starting point and the freeze bond setting was applied to the atoms where bonds are formed via the Edit-->Reduntant Coordinates function. Bond angles could be set by clicking on the Modify bond tool in Gaussview. It could also be set by opening the source file of the input file and adding the line B 5 1 2.2 B as follows:

<pre>

# opt=modredundant hf/3-21g geom=connectivity

chair_redundantcoord_opt

0 1
H -0.66453632 -0.95596654 0.02282130
C 0.16493709 0.24828195 1.55946699
H -0.15623149 1.16872620 1.10416522
H 0.31899234 0.31979573 2.62024283
C 0.15890254 -2.16405336 1.55952069
H 0.31297285 -2.23629359 2.62019230
H -0.16733038 -3.08276068 1.10410851
C -0.27336372 -0.95691982 1.02501257
H 3.11613426 -0.96491980 2.53704339
C 2.28666084 -2.16916829 1.00039771
H 2.60782942 -3.08961254 1.45569948
H 2.13260560 -2.24068207 -0.06037814
C 2.29269540 0.24316702 1.00034400
H 2.13862509 0.31540725 -0.06032760
H 2.61892832 1.16187434 1.45575618
C 2.72496165 -0.96396652 1.53485212

1 8 1.0
2 3 1.0 4 1.0 8 1.5
3
4
5 6 1.0 7 1.0 8 1.5
6
7
8
9 16 1.0
10 11 1.0 12 1.0 16 1.5
11
12
13 14 1.0 15 1.0 16 1.5
14
15
16

B 2 13 F
B 2 13 2.2 B
B 5 10 F
B 5 10 2.2 B

</pre>

[[File:Chair ts redcoord.png|200px]]

Thereafter, the guess structure is optimised to a minimum using the same basis set as before and a similar optimised structure is obtained except that the bond lengths between the bonds that are supposed to form are fixed are 2.2 Å.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Chair Optimisation (Freeze Bond) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61518450
|-
| Gradient || 0.00324925 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2h

Link:[[Media:CHAIR REDUNDANTCOORD OPT.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001587 0.001800 YES
RMS Displacement 0.000416 0.001200 YES
Predicted change in Energy=-6.425287D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was slightly higher at -231.61518450 au compared to -231.61932239 au obtained for the previous optimisation. This is due to the frozen bonds that are not at their optimum bond lengths. The rest of the molecule is nonetheless optimised to their minimum. The molecule can now be unfrozen at the reaction centres and optimized again, this time to a transition state and not a minimum.

===== Unfreezing the frozen bonds =====

The output file with frozen bonds is copied into a new molecule window and the frozen bonds are now unfrozen by changing the redundant coordinates to Bond Derivative, which utilises the Hessian. The optimisation set up involved the following set-up:

Job type: Opt+Freq 
Optimize to a: TS (berny) 
Calculate Force Constants: Never 
Keywords: opt=(noeigen, catesian) 

Method: Hartree Fock 
Basis Set: 3-21g

{| class="wikitable" border="1"
|+
! Unfrozen Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932228
|-
| Gradient || 0.00003916 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 7 sec
|}

Link: [[Media:Chair derivative opt.out]]

Symmetry : Ci

<pre>

Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-1.935288D-07
Optimization completed.
-- Stationary point found.

</pre>

The optimisation was successful as convergence to a transition state was achieved. However energy obtained was -231.61932228 au, lower than the -231.61518450 au obtained for the frozen bond optimisation, which was expected and comparable to -231.61932239 au obtained for the previous optimisation without using the redundant coordinate method.

The bond forming/bond breaking bond lengths of the optimisations are both at 2.02 Å. As such, we can conclude both methods (with or without redundant coordinate) are reasonable transition state optimisation methods as long as the guess structure at the beginning is good enough, which remains the most crucial part of transition state optimisation.

[[File:Chair derivative vib.gif|250px]]

A similar imaginary vibration is also obtained for this optimisation at -817.85 cm-1, indicative of a transition state. Upon animation, we observe that the vibration corresponds to the Cope rearrangement, via a chair transition state.

==== Optimizing and Frequency Analysis of Boat TS ====

The boat transition state is obtained by a very different method from the chair transition state. A method called QST2 is employed.

===== Failed Attempt: Wrong reactant/product geometry =====

Firstly, the optmised anti2 1,5-hexadiene (the reactant molecule) is opened and copied and pasted into a new molecule screen. A 2nd molecule is pasted in the same MolGroup, that allows it to be displayed side-by-side in the same molecule screen as follows. The numberings on the C & H atoms are also rearranged such that the molecule on the right tab is a Cope-rearrangement product of that in the left tab. This rearrangement can be done by editing the Atom List parameters in a running order from atom 16-1.

[[File:Boat guess.png|300px]]

Upon rearrangement, a QST2 calculation can be set up using the following set-up details:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2 -- failed) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.61932234
|-
| Gradient || 0.00004373 au
|-
| Dipole Moment || 0.0002 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 8 sec
|}

Symmetry: Ci

Link:[[Media:BOAT TS GUESS2.LOG]]

This optimisation is however failed as the output generated is a chair optimisation geometry and the chk file shows that the bonds forming on the respective ends have crossed one another so that the boat structure is converted over to the chair. Thus, though convergence was achieved, it had gone through a different transtion state (i.e. chair instead of boat)

[[File:Boat fail.png|200px]]

===== Successful Attempt: Modified reactant/product geometry =====

The failure is due to the starting geometry of anti2 hexadiene being a wrong starting point for the optimisation. Thus, a more accurate geometry is required for the reactant and product molecules is required. This can be done by rotating the central C-C-C-C dihedral angle of 1,5-hexadiene from 180o to 0o, changing the inside C-C-C angle of C2-C3-C4 and C3-C4-C5 of the reactant molecule and reduce them to 100o. The same is done to the product molecule and they should end up like the screenshot below. The hydrogen groups will also need to be adjusted so that they are in the correct orientations and are numbered correctly with respect to the attached carbon.

[[File:Boat guess2.png|300px]]

Upon realigning of geometry, the new product and reactant molecules can be optimised via the same method and the correct boat transtion state should be attained.

Method: Hartree Fock 
Basis Set: 3-21G

{| class="wikitable" border="1"
|+
! Boat Optimisation (QST2) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.60280212
|-
| Gradient || 0.00003958 au
|-
| Dipole Moment || 0.1585 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 9 sec
|}

Symmetry: C2V

Link:[[Media:BOAT TS GUESS3.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000067 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.000974 0.001800 YES
RMS Displacement 0.000275 0.001200 YES
Predicted change in Energy=-1.185167D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

Low frequencies --- -840.2505 -3.5563 -2.9068 0.0004 0.0005 0.0006
Low frequencies --- 5.8078 155.3524 382.3394
****** 1 imaginary frequencies (negative Signs) ******

There is also 1 imaginary vibration obtained at frequency -840.2505 cm-1, indicative of a transition state. Display of vibrations showed that the imaginary frequency at -840.2505 cm-1 corresponds to the Cope-rearrangement, proceeding via a boat transition state.

[[File:Boat negative vib.gif|300px]]

QST2 method has proven to be useful as it is a fully automated process but it often fails if the reactant and products are not close to the transition structure as seen in the case of the original anti2 1,5-hexadiene.

==== IRC Analysis ====

In order to predict the conformer that the transition structure will lead to eventually, we need to monitor the reaction pathway and this can be done by using the Intrinsic Reaction Coordinates (IRC) method that allows the following of the minimum energy path from the transition structure down to its local minimum. It creates a series of points by taking small geometry steps in the direction where the gradient is the steepest, leading to either the final product or reactant.

Due to the symmetry of the reaction coordinates in the Cope rearrangement, we could just observe the IRC coordinate in the forward direction.

===== IRC Analysis (Chair TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 50

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:Irc chair forward.gif|250px]]

The IRC above shows that the chair transition state leads to a gauche conformer of product 1,5-hexadiene. However, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69166702
|-
| Gradient || 0.00000474 au
|-
| Dipole Moment || 0.3806 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 12 sec
|}

Symmetry: C2

Link:[[Media:IRC LASTPT MIN.LOG]]

[[File:Irc final pt.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000300 0.001800 YES
RMS Displacement 0.000091 0.001200 YES
Predicted change in Energy=-2.405616D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69166702 au) and geometry (C2) obtained corresponds to the gauche2 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]].

===== IRC Analysis (Boat TS)=====

The IRC is set up as follows: 

Job type: IRC
Follow IRC: Forward Only
Force Constants: Calculate Always
Compute more points, N = 100 -- A higher N is inserted for this calculation to get a better minimum at the end of the IRC run.

Method: Hartree-Fock
Basis-Set: 3-21G

[[File:IRC boat Pathway.gif|250px]]

The IRC above shows that the boat transition state leads to another gauche conformer of product 1,5-hexadiene. However, as with the previous IRC run, the last point of the IRC is often not the minimum and needs further optimisation to a minimum such that the low energy conformer can be determined.

An optimisation to a minimum is set up as follows:

Method: Hartree-Fock
Basis-Set: 3-21G

{| class="wikitable" border="1"
|+
! Optimisation (Last point IRC -- Boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final energy in atomic units (au) || -231.69266120
|-
| Gradient || 0.000001184 au
|-
| Dipole Moment || 0.3407 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 18 sec
|}

Symmetry: C1

Link:[[Media:IRC BOAT LASTPTMIN.LOG]]

[[File:Boat finalpt irc.png|200px]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000284 0.001200 YES
Predicted change in Energy=-1.955451D-08
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved in this optimisation and the final energy (-231.69266120 au) and geometry (C1) obtained corresponds to the gauche3 low energy conformer from [[Mod:phys3#Appendix 1|Appendix 1]]. The gauche3 low energy conformer of 1,5-hexadiene is the lowest energy conformer.

==== Re-optimisation of TS using higher basis set ====

In order to calculate activation energies of the different transition states, we need a more accurate optimisation of the transition states. A higher basis set is now used to improve the accuracy. Geometries obtained for both the chair and boat transition states are unchanged but energy levels have been lowered significantly in both cases.

===== Re-optimisation of TS using higher basis set (CHAIR TS) =====

A previously optimised Chair TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (chair TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.55698286
|-
| Gradient || 0.00004909 au
|-
| Dipole Moment || 0.0000 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 2 min 54 sec
|}

Symmetry: C2v

Link: [[Media:CHAIR TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.001543 0.001800 YES
RMS Displacement 0.000640 0.001200 YES
Predicted change in Energy=-3.220993D-07
Optimization completed.
-- Stationary point found.
GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.414927
Sum of electronic and thermal Energies= -234.409006
Sum of electronic and thermal Enthalpies= -234.408062
Sum of electronic and thermal Free Energies= -234.443812

===== Re-optimisation of TS using higher basis set (BOAT TS) =====

A previously optimised Boat TS was chosen and used in this re-optimisation. The re-optimisation set-up is as follows:

Job type: Opt+Freq 
Optimize to a: TS(QST2)
Calculate Force Constant: Never

Method: DFT/B3LYP 
Basis Set: 6-31Gd

{| class="wikitable" border="1"
|+
! Reoptimisation (boat TS) !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G(d)
|-
| Final energy in atomic units (au) || -234.54309307
|-
| Gradient || 0.00000409 au
|-
| Dipole Moment || 0.0613 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 8 min 36 sec
|}

Symmetry: C2

Link: [[Media:BOAT TS 631GD.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000009 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000148 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-2.755574D-09
Optimization completed.
-- Stationary point found.

</pre>

Convergence is achieved and the transition state energy level obtained using this basis set has lowered rather significantly.

===== Thermochemistry =====

Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431752

==== Thermochemical Analysis ====

===== Summary of energies =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| '''
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -234.556983
| align="center" | -234.414927
| align="center" | -234.409006
|-
| '''Boat TS'''
| align="center" | -234.543093
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -234.611703
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 a.u. = 627.509 kcal/mol 

===== Activation energies (in kcal/mol) =====

{| border="1" cellspacing="1" cellpadding="10"
|-
| '''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}
 
The activation energies obtained from the 6-31G(d) basis set is quite close to the energies obtained via experiment. Therefore, it can be determined that the basis set is good enough for thermodynamic analysis. The activation energy of the energy pathway going through the boat transition state also gives a higher ΔE compared to the chair. This is expected as the boat structure is a less stable transition state compared to the corresponding chair structure. Given that the 3-21G basis set differs from the 6-31G(d) basis set quite significantly, it is likely to be highly inaccurate in the determination of ΔE.

== Week 2 ==

=== Diels-Alder: Cyclohexene ===

The formation of cyclohexene involves the most basic Diels-Alder cycloaddition of cisbutadiene and ethene. By optimising the transition state of the reaction, we are able to follow the reaction pathway and determine the symmetric properties of the HOMO and LUMO.

==== Optimisation of cis-butadiene ====

[[File:Butadiene opt.png|200px]]

Cis-butadiene was optimised via the following setup:

Job-Type: Opt+Freq 
Optimise to a: Minimum
Calculate force Constants: Never

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.04879734
|-
| Gradient || 0.00008900 au
|-
| Dipole Moment || 0.0414 Debye
|-
| Point Group || C2
|-
| Calculation Time Taken || 0 min 5 sec
|}

Symmetry: C2v

Link:[[Media:CISBUTADIENE1.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000783 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540844D-07
Optimization completed.
-- Stationary point found.

</pre>

Convergence has been achieved.

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:Butadiene homo.png|250px]]
| style="text-align: center;|[[File:Butadiene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

==== Optimisation of ethylene+cis-butadiene transition state ====

Ethylene and cis-butadiene transition state can be derived from inserting the guess structure of transition state for their formation of cyclohexene.

[[File:Cyclohexene ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: opt=(noeigen)

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! Cyclohexene_TS !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || 0.11165465
|-
| Gradient || 0.00000783 au
|-
| Dipole Moment || 0.5605 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Symmetry: Cs

Link:[[Media:CYCLOHEXENE TS.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000067 0.001200 YES
Predicted change in Energy=-2.398935D-09
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -956.3610 -0.0527 -0.0240 -0.0032 1.6468 3.1387
Low frequencies --- 3.6666 147.2610 246.6152
****** 1 imaginary frequencies (negative Signs) ******

Convergence has been achieved. 1 imaginary frequency has been observed at -956.3610 cm-1 indicative of a transition state. An animation of the imaginary vibration below resembles that of a Diels Alder transition state as well. This vibrational illustration also shows that the cycloaddition process is a synchronous one.

[[File:Cyclohexene ts.gif|250px]]

{| class="wikitable" border="1"
|+
! HOMO !! LUMO
|-
| style="text-align: center;|[[File:TS butadiene ethene homo.png|250px]]
| style="text-align: center;|[[File:TS butadiene ethene lumo.png|250px]]
|-
! AntiSymmetric !! Symmetric
|}

[[File:Cyclohexene ts2.png|200px]]

===== Discussion =====

 

The transition state structure shows the geometry of a slightly distorted tetrahedral structure about the bond forming carbons as they are switching from the original sp2 hybridisation to sp3 hybridisation. The ethene molecule approaches the planar cis-butadiene at an angle of 100o, which resembles the Bürgi-Dunitz trajectory, where orbital overlap is maximised.

 

Bond lengths of the partly formed σ C-C bonds are 2.11920 Å which is longer than a typical sp3 C-C bond length (1.54 Å) or sp2 C=C bond length (1.64 Å). Van der Waals radius of the C atom is 1.70 Å. Therefore, for 2 adjacent C atoms that do not interact, the total radii is 3.40 Å In the partly formed σ C-C bonds, the bond lengths obtained are shorter than the total radii of 2 non-interacting C atoms indicative of attractive forces and orbital overlap between the two carbon atoms, though insufficient to fully form a C-C bond formally.

 

As mentioned above, the formation of two bonds are synchronous. The lowest positive frequency,in comparison, is found to be at 147.2610 cm-1, which resembles a rocking motion of the ethene molecule and minimal indication with cis-butadiene. It also does not show any indication of any transition state structure. This is expected as positive vibrational frequencies represent a local minimum and not a transition state unlike imaginary frequencies.

 

The HOMO at the transition structure is antisymmetric. The cycloaddition involves the interaction between HOMO of butadiene (antisymmetric) and LUMO of ethene (antisymmetric) This reaction is allowed as the both butadiene and ethene frontier orbitals have the same antisymmetric property and are relatively close in energy and they are able to match and overlap effectively in space. The closeness in energy would be further enhanced if the ethene LUMO is stabilised by electron-withdrawing groups. The lowering of LUMO energy will allow it to overlap even more effectively with the butadiene HOMO, and result in a lower transition state. This explains why maleic anhydride, with (-C(=O)-O-C(=O)-) attached to ethene component, makes such a good dienophile.

==== Cyclohexa-1,3-diene with maleic anhydride ====

The Diels Alder cycloaddition of cyclohexa-1,3-diene with maleic anhydride is more complex than that of cyclohexene as there is the possibility of obtaining either the exo or endo products. This difference arises from the fact that the C-C bonds can be formed from the top face of maleic anhydride (exo) or from the bottom face of maleic anhydride (endo). Theoretically, the endo form goes through a more stable transition state, thus is the preferred kinetic product, though the exo product is the more stable thermodynamic product. This could be proven computationally by examining the relative energies of the exo and endo transition structures.

===== Optimising the Exo transition state =====

A guess structure for the exo transition state is constructed to resemble the exo product molecule, with slightly longer bond lengths between the bonding forming carbon atoms (~2.2 Å). The exo transition state of the reaction is optimised via the following set-up:

[[File:Exo ts.png|200px]]

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! exo TS optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

Link: [[Media:EXO TS 2.LOG]]

<pre>

Item Value Threshold Converged?
Maximum Force 0.000101 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.000383 0.001200 YES
Predicted change in Energy=-7.584071D-08
Optimization completed.
-- Stationary point found.

</pre>

Low frequencies --- -812.2953 -2.4172 -2.0775 -0.4799 -0.0047 0.4370
Low frequencies --- 1.3050 60.7997 123.8552
****** 1 imaginary frequencies (negative Signs) ******

Converged have been achieved. Frequency analysis gives an imaginary frequency at -812.2953 cm-1, indicative of a transition state. The visualisation of the imaginary frequency shows the suprafacial nature of the concerted cycloaddition.#

[[File:Exo ts vib.gif|250px]]

Symmetry: Cs

===== Optimising the Endo transition state =====

The guess structure of the endo transition state is constructed by copying the exo guess structure and rotating the maleic anhydride molecule around such that the -(C=O)-O-(C=O)- fragment lies below the diene component of cyclohexa-1,3-diene.

Job-Type: Opt+Freq 
Optimise to a: TS (Berny)
Calculate force Constants: Once
Keywords: Opt=noeigen

Method: Semi-empirical/AM1

{| class="wikitable" border="1"
|+
! cis-butadiene Optimisation !!
|-
| File type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RAM1
|-
| Basis Set || ZDO
|-
| Final energy in atomic units (au) || -0.05041979
|-
| Gradient || 0.00002406 au
|-
| Dipole Moment || 5.5647 Debye
|-
| Point Group || C1
|-
| Calculation Time Taken || 0 min 3 sec
|}

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').
Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?
Look at published examples and investigate further if you have time.