= Transition States Computational Lab =

=== Introduction: Transition States ===
A transition state is an instantaneous state that molecules go through during a reaction between products and reactants; it cannot be detected by spectroscopic methods. In the context of a potential energy surface, it is a saddle point, the highest energy point (maximum) on the surface, with a gradient of zero (i.e. dy/dx = 0) and a negative curvature (i.e. d2y/dx2 =-ve). A minimum is the lowest energy point on a potential energy surface and corresponds to physically stable chemical species, with a gradient of zero (i.e. dy/dx = 0) and a positive curvature (i.e. d2y/dx2 =+ve).

=== Exercise 1: Reaction of Butadiene with Ethylene ===

The reaction between Butadiene and Ethylene is a Diels-Alder reaction which proceeds via a cyclic transition state, as shown below in Scheme 1:
[[File:Reaction_Scheme_GIF_cm3414.png|500 px|thumb|centre|Scheme 1: Reaction of Butadiene and Ethene]]

==== Molecular Orbitals ====
The MO diagram for this reaction, including basic symmetry labels, is shown below in Fig. 1. In this reaction the diene (butadiene) LUMO and dieneophile (ethene) HOMO are close in energy, which results in a bonding interaction between the two and forms the HOMO and LUMO of the TS. This is an inverse electron demand reaction:

[[File:Diels-Alder MO.gif|600 px|thumb|centre|Figure 1: MO diagram for Butadiene, Ethene, and the Transition State]]

An inverse electron demand is confirmed by visualisation of the MOs in Gaussview. The HOMOs and LUMOs of ethene and butadiene are shown below, which correlate to those shown on the MO diagram above:
[[File:Ethene_and_Butadiene_MOs_cm3414.png|600 px|thumb|centre|Figure 2: Frontier Orbitals of Ethene and Butadiene]]

Visualisation of the TS MOs allows them to be correlated to those shown in the MO diagram. Below the TS HOMO and LUMO are shown, which, as illustrated, clearly correlate to the in-phase and out-of-phase interaction of the diene LUMO and dieneophile HOMO:
[[File:TS_HOMO_CM3414.jpg|300 px|thumb|centre|Figure 3: Transition State HOMO]]
[[File:TS_LUMO_cm3414.jpg|300 px|thumb|centre|Figure 4: Transition State LUMO]]

This confirms an inverse electron demand, i.e. that it is indeed the dieneophile HOMO and diene LUMO which are closest in energy and interact to from the TS HOMO and LUMO.

From the MO diagram shown above in Fig. 1, conclusions can be made about the symmetry requirements of a reaction. Only those orbitals which are of the same symmetry, i.e. both symmetric or both asymmetric, can give an allowed reaction. An interaction between a S and AS orbital is forbidden. This is because the overlap integral for an AS-AS or S-S interaction is non-zero, whereas that for an AS-S interaction is zero.

==== Bond Lengths ====

The progression of the reaction can be viewed in terms of the changing bond lengths.
Typical C-C bond lengths are also shown in Table 1.
{| class="wikitable" border="1"
|+ Table 1: Typical Carbon-Carbon Bond Lengths/ Å
! sp3-sp3 !! sp3-sp2 !! sp2-sp2
|-
| 1.45 || 1.50 || 1.33
|}

The changes in bond lengths as the Diels-Alder reaction between ethene and butadiene are shown below in Fig. 5 from the reactants, through the transition state, and to the products.

[[File:Bond_lengths_cm3414.gif|700 px|thumb|centre|Figure 5: Change in Bond Lengths as the Diels-Alder reaction progresses]]

It can be seen that as the reaction progresses, the double bonds in butadiene change to single bonds and lengthen from 1.335-1.501 A. The single bond in butadiene transform to a double bond and shortens from 1.468-1.338 A. The bond length of ethene also increases, from 1.327-1.540 A. The reactants were initially separated by 2.200 where new C-C bonds would form, and this shortens to 1.541 as the bonds form.
These bond lengths roughly match those expected both in the products and reactants, with the bond lengths in the transition state all being intermediate between the expected lengths in the reactant and product.
The Van der Waals radius of a C atom is 1.7 A, which means that a bonding interaction would occur between C atoms which are less than 2.4 A apart, indicating that in the TS the newly forming C-C bonds are definitely experiencing a bonding interaction.

==== Transition State Vibrations ====

The vibration shown below in Fig. 6 is that which corresponds to the reaction path at the transition state. In Gaussview it appears as an imaginary vibration at -948.48. It shows that the formation of the two bonds is synchronous.

[[File:TS_Imaginary_Vibration_cm3414.gif|400px|thumb|centre|Figure 6 Transition State Vibration]] '''''Note:''' for an unknown reason wiki would not upload the animated vibration gifs, however the file can be viewed here:'' [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TS_Imaginary_Vibration_cm3414.gif https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TS_Imaginary_Vibration_cm3414.gif]

Conversely, the lowest positive (i.e. real, not imaginary) frequency is 145.12 and is asynchronous, with the molecule of ethene twisting towards one end of the butadiene molecule:

[[File:TS_lowest_positive_vibration_cm3414.gif|thumb|400px|centre|Figure 7 Lowest Positive Vibration]] '''''Note:''' for an unknown reason wiki would not upload the animated vibration gifs, however the file can be viewed here:'' [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TS_lowest_positive_vibration_cm3414.gif https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TS_lowest_positive_vibration_cm3414.gif]

=== Exercise 2: Reaction of 1,3-Diaxole with Cyclohexadiene ===

[[File:Ex2_Reaction_Scheme.png|600 px|thumb|centre|Scheme 2: The Reaction of 1,3-Dioxole with Cyclohexadiene]]

==== MO Diagram ====
The HOMOs and LUMOs of 1,3-dioxole and
cyclohexadiene are shown below, and beneath that are the HOMOs and LUMOs of the transition states in both the endo and exo products. The MO diagram of this reaction is similar to that shown in Figure 2, with 1,3-dioxole acting as the diene and cyclohexadiene the dieneophile.

[[File:Ex2_Reactants_TS_MOs.png|600 px|thumb|centre|Figure 8: Molecular Orbitals of 1,3-Dioxole and Cyclohexadiene]]
[[File:Ex2_Reactants_TS_MOs.png|600 px|thumb|centre|Figure 9: Molecular Orbitals of the Endo and Exo TSs]]

As shown by the MOs of the transition states, both the HOMO and LUMOs have a plane of symmetry, therefore were formed from the symmetrical orbitals of the reactants, i.e. the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene. This is an inverse electron demand reaction in which the dieneophile is the lower energy component and donates electron density into the empty LUMO of the diene. This is known to occur when there is an electron withdrawing group on the diene (i.e. two electronegative oxygen atoms in this case) or an electron donating group on the dieneophile. These characteristics mean that the dieneophile HOMO and diene LUMO are now the closest energy orbitals of the same symmetry which can interact.

==== Reaction Barrier Energies ====

The energies of the of the reactants, transition states and products were found by viewing the text files of the .log files. These energies are tabulated below in Table 2:

{| class="wikitable" border="1"
|+ Table 2: Energies in Reaction of 1,3-Dioxole and Cyclohexadiene (kJ/mol)

! Reactants !! Endo TS !! Exo TS !! Endo Product !! Exo Product
|-
| 195.49 || 362.16 || 364.69 || 99.25 || 99.70
|}

These energies can be used to find the reaction barriers and reaction energies. The enthalpy change for the reaction is given by the difference between the reactants and products. For the endo reaction it is -96.21 kJ/mol, and for the exo reaction it is -95.79 kJ/mol. The endo reaction is slightly more exothermic than the exo and the product is slightly lower in energy, which means that the endo product is thermodynamically more stable (by a small amount).

The reaction barriers can be found by finding the difference between the reactants and the transition states, which for the endo product is 166.67 kJ/mol and for the exo product is 169.2 kJ/mol. The endo product has a lower reaction barrier since the transition state is lower in energy. The reasons for this are discussed in the next part of this section.

==== Secondary Orbital Interactions ====

Secondary Orbital Interactions are interactions between non-bonding orbitals, which can have a stabilising effect on the system and lower its overall energy. In the HOMO of the endo product in the reaction between 1,3-dioxole and cyclohexadiene there are secondary orbital interactions between the oxygen atoms on 1,3-dioxole and the pi orbitals at the back of the diene which lower the energy in the transition state. This can occur because the orbitals have the correct orientation in the endo form, whereas in the exo form the oxygen atoms are not near the back of the diene and there are only primary orbital interactions in the exo product. These differences are illustrated in the TS HOMOs shown below:

[[File:Secondary_Orbital_Interactions.png|600 px|thumb|centre|Figure 10: Secondary Orbital Interactions]]

=== Exercise 3: Diels-Alder vs. Chelotropic ===

Xylylene and Sulfur Dioxide can undergo a variety of cycloaddition reactions to give different products. Xylylene, an unstable molecule, acts as the diene, and SO2 as the dieneophile. The reaction can proceed via an endo- or exo- Diels-Alder or via a Chelotropic Mechanism. These three possible outcomes are shown below in Scheme 2:

[[File:Reaction_Scheme_cm3414.gif|500 px|thumb|centre|Scheme 2: Outcomes of reaction of Xylylene with Sulfur Dioxide]]

==== IRC Calculations ====
In this exercise, the products, TSs and reactants were optimised at the PM6 level using Gaussview and IRC calculations were carried out for each pathway. These IRCs are shown below:

[[File:Exo_da_irc_cm3414.png|600 px|thumb|centre|Figure 8: Exo Diels-Alder IRC]]
[[File:Endo_da_irc_cm3414.png|600 px|thumb|centre|Figure 9: Endo Diels-Alder IRC]]
[[File:chelotropic_irc_cm3414.png|600 px|thumb|centre|Figure 10: Chelotropic IRC]]

==== Energy Profiles ====
The activation energies and reaction energies could be calculated (in kJ/mol) and used to draw reaction profiles of each of these reactions. These are shown below.

[[File:Exo-Diels_Alder_Reaction_Profile_cm3414.gif|600 px|thumb|centre|Figure 11: Exo Diels-Alder Reaction Profile]]
[[File:Endo-Diels_Alder_Reaction_Profile_cm3414.gif|600 px|thumb|centre|Figure 12: Endo Diels-Alder Reaction Profile]]
[[File:Chelotropic_Reaction_Profile_cm3414.gif|600 px|thumb|centre|Figure 13: Chelotropic Reaction Profile]]

This shows that the preferred reaction route (provided the reaction is irreversible) is the endo Diels-Alder reaction, since reaction has the lowest activation energy (this is the kinetic product). The exo Diels-Alder reaction produces product which is thermodynamically more stable than the endo, however the product of the chelotropic reaction is lowest in energy and therefore the most thermodynamically stable.

File:Ex2 Reaction Scheme.png

2016-12-08T16:06:44Z

Cm3414:

Rep:Mod:cm3414

2016-12-08T15:58:01Z

Cm3414: /* Secondary Orbital Interactions */

= Transition States Computational Lab =

=== Introduction: Transition States ===
A transition state is an instantaneous state that molecules go through during a reaction between products and reactants; it cannot be detected by spectroscopic methods. In the context of a potential energy surface, it is a saddle point, the highest energy point (maximum) on the surface, with a gradient of zero (i.e. dy/dx = 0) and a negative curvature (i.e. d2y/dx2 =-ve). A minimum is the lowest energy point on a potential energy surface and corresponds to physically stable chemical species, with a gradient of zero (i.e. dy/dx = 0) and a positive curvature (i.e. d2y/dx2 =+ve).

=== Exercise 1: Reaction of Butadiene with Ethylene ===

The reaction between Butadiene and Ethylene is a Diels-Alder reaction which proceeds via a cyclic transition state, as shown below in Scheme 1:
[[File:Reaction_Scheme_GIF_cm3414.png|500 px|thumb|centre|Scheme 1: Reaction of Butadiene and Ethene]]

==== Molecular Orbitals ====
The MO diagram for this reaction, including basic symmetry labels, is shown below in Fig. 1. In this reaction the diene (butadiene) LUMO and dieneophile (ethene) HOMO are close in energy, which results in a bonding interaction between the two and forms the HOMO and LUMO of the TS. This is an inverse electron demand reaction:

[[File:Diels-Alder MO.gif|600 px|thumb|centre|Figure 1: MO diagram for Butadiene, Ethene, and the Transition State]]

An inverse electron demand is confirmed by visualisation of the MOs in Gaussview. The HOMOs and LUMOs of ethene and butadiene are shown below, which correlate to those shown on the MO diagram above:
[[File:Ethene_and_Butadiene_MOs_cm3414.png|600 px|thumb|centre|Figure 2: Frontier Orbitals of Ethene and Butadiene]]

Visualisation of the TS MOs allows them to be correlated to those shown in the MO diagram. Below the TS HOMO and LUMO are shown, which, as illustrated, clearly correlate to the in-phase and out-of-phase interaction of the diene LUMO and dieneophile HOMO:
[[File:TS_HOMO_CM3414.jpg|300 px|thumb|centre|Figure 3: Transition State HOMO]]
[[File:TS_LUMO_cm3414.jpg|300 px|thumb|centre|Figure 4: Transition State LUMO]]

This confirms an inverse electron demand, i.e. that it is indeed the dieneophile HOMO and diene LUMO which are closest in energy and interact to from the TS HOMO and LUMO.

From the MO diagram shown above in Fig. 1, conclusions can be made about the symmetry requirements of a reaction. Only those orbitals which are of the same symmetry, i.e. both symmetric or both asymmetric, can give an allowed reaction. An interaction between a S and AS orbital is forbidden. This is because the overlap integral for an AS-AS or S-S interaction is non-zero, whereas that for an AS-S interaction is zero.

==== Bond Lengths ====

The progression of the reaction can be viewed in terms of the changing bond lengths.
Typical C-C bond lengths are also shown in Table 1.
{| class="wikitable" border="1"
|+ Table 1: Typical Carbon-Carbon Bond Lengths/ Å
! sp3-sp3 !! sp3-sp2 !! sp2-sp2
|-
| 1.45 || 1.50 || 1.33
|}

The changes in bond lengths as the Diels-Alder reaction between ethene and butadiene are shown below in Fig. 5 from the reactants, through the transition state, and to the products.

[[File:Bond_lengths_cm3414.gif|700 px|thumb|centre|Figure 5: Change in Bond Lengths as the Diels-Alder reaction progresses]]

It can be seen that as the reaction progresses, the double bonds in butadiene change to single bonds and lengthen from 1.335-1.501 A. The single bond in butadiene transform to a double bond and shortens from 1.468-1.338 A. The bond length of ethene also increases, from 1.327-1.540 A. The reactants were initially separated by 2.200 where new C-C bonds would form, and this shortens to 1.541 as the bonds form.
These bond lengths roughly match those expected both in the products and reactants, with the bond lengths in the transition state all being intermediate between the expected lengths in the reactant and product.
The Van der Waals radius of a C atom is 1.7 A, which means that a bonding interaction would occur between C atoms which are less than 2.4 A apart, indicating that in the TS the newly forming C-C bonds are definitely experiencing a bonding interaction.

==== Transition State Vibrations ====

The vibration shown below in Fig. 6 is that which corresponds to the reaction path at the transition state. In Gaussview it appears as an imaginary vibration at -948.48. It shows that the formation of the two bonds is synchronous.

[[File:TS_Imaginary_Vibration_cm3414.gif|400px|thumb|centre|Figure 6 Transition State Vibration]] '''''Note:''' for an unknown reason wiki would not upload the animated vibration gifs, however the file can be viewed here:'' [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TS_Imaginary_Vibration_cm3414.gif https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TS_Imaginary_Vibration_cm3414.gif]

Conversely, the lowest positive (i.e. real, not imaginary) frequency is 145.12 and is asynchronous, with the molecule of ethene twisting towards one end of the butadiene molecule:

[[File:TS_lowest_positive_vibration_cm3414.gif|thumb|400px|centre|Figure 7 Lowest Positive Vibration]] '''''Note:''' for an unknown reason wiki would not upload the animated vibration gifs, however the file can be viewed here:'' [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TS_lowest_positive_vibration_cm3414.gif https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:TS_lowest_positive_vibration_cm3414.gif]

=== Exercise 2: Reaction of 1,3-Diaxole with Cyclohexadiene ===

==== MO Diagram ====
The HOMOs and LUMOs of 1,3-dioxole and
cyclohexadiene are shown below, and beneath that are the HOMOs and LUMOs of the transition states in both the endo and exo products. The MO diagram of this reaction is similar to that shown in Figure 2, with 1,3-dioxole acting as the diene and cyclohexadiene the dieneophile.

[[File:Ex2_Reactants_TS_MOs.png|600 px|thumb|centre|Figure 8: Molecular Orbitals of 1,3-Dioxole and Cyclohexadiene]]
[[File:Ex2_Reactants_TS_MOs.png|600 px|thumb|centre|Figure 9: Molecular Orbitals of the Endo and Exo TSs]]

As shown by the MOs of the transition states, both the HOMO and LUMOs have a plane of symmetry, therefore were formed from the symmetrical orbitals of the reactants, i.e. the HOMO of 1,3-dioxole and the LUMO of cyclohexadiene. This is an inverse electron demand reaction in which the dieneophile is the lower energy component and donates electron density into the empty LUMO of the diene. This is known to occur when there is an electron withdrawing group on the diene (i.e. two electronegative oxygen atoms in this case) or an electron donating group on the dieneophile. These characteristics mean that the dieneophile HOMO and diene LUMO are now the closest energy orbitals of the same symmetry which can interact.

==== Reaction Barrier Energies ====

The energies of the of the reactants, transition states and products were found by viewing the text files of the .log files. These energies are tabulated below in Table 2:

{| class="wikitable" border="1"
|+ Table 2: Energies in Reaction of 1,3-Dioxole and Cyclohexadiene (kJ/mol)

! Reactants !! Endo TS !! Exo TS !! Endo Product !! Exo Product
|-
| 195.49 || 362.16 || 364.69 || 99.25 || 99.70
|}

These energies can be used to find the reaction barriers and reaction energies. The enthalpy change for the reaction is given by the difference between the reactants and products. For the endo reaction it is -96.21 kJ/mol, and for the exo reaction it is -95.79 kJ/mol. The endo reaction is slightly more exothermic than the exo and the product is slightly lower in energy, which means that the endo product is thermodynamically more stable (by a small amount).

The reaction barriers can be found by finding the difference between the reactants and the transition states, which for the endo product is 166.67 kJ/mol and for the exo product is 169.2 kJ/mol. The endo product has a lower reaction barrier since the transition state is lower in energy. The reasons for this are discussed in the next part of this section.

==== Secondary Orbital Interactions ====

Secondary Orbital Interactions are interactions between non-bonding orbitals, which can have a stabilising effect on the system and lower its overall energy. In the HOMO of the endo product in the reaction between 1,3-dioxole and cyclohexadiene there are secondary orbital interactions between the oxygen atoms on 1,3-dioxole and the pi orbitals at the back of the diene which lower the energy in the transition state. This can occur because the orbitals have the correct orientation in the endo form, whereas in the exo form the oxygen atoms are not near the back of the diene and there are only primary orbital interactions in the exo product. These differences are illustrated in the TS HOMOs shown below:

[[File:Secondary_Orbital_Interactions.png|600 px|thumb|centre|Figure 10: Secondary Orbital Interactions]]

=== Exercise 3: Diels-Alder vs. Chelotropic ===

Xylylene and Sulfur Dioxide can undergo a variety of cycloaddition reactions to give different products. Xylylene, an unstable molecule, acts as the diene, and SO2 as the dieneophile. The reaction can proceed via an endo- or exo- Diels-Alder or via a Chelotropic Mechanism. These three possible outcomes are shown below in Scheme 2:

[[File:Reaction_Scheme_cm3414.gif|500 px|thumb|centre|Scheme 2: Outcomes of reaction of Xylylene with Sulfur Dioxide]]

==== IRC Calculations ====
In this exercise, the products, TSs and reactants were optimised at the PM6 level using Gaussview and IRC calculations were carried out for each pathway. These IRCs are shown below:

[[File:Exo_da_irc_cm3414.png|600 px|thumb|centre|Figure 8: Exo Diels-Alder IRC]]
[[File:Endo_da_irc_cm3414.png|600 px|thumb|centre|Figure 9: Endo Diels-Alder IRC]]
[[File:chelotropic_irc_cm3414.png|600 px|thumb|centre|Figure 10: Chelotropic IRC]]

==== Energy Profiles ====
The activation energies and reaction energies could be calculated (in kJ/mol) and used to draw reaction profiles of each of these reactions. These are shown below.

[[File:Exo-Diels_Alder_Reaction_Profile_cm3414.gif|600 px|thumb|centre|Figure 11: Exo Diels-Alder Reaction Profile]]
[[File:Endo-Diels_Alder_Reaction_Profile_cm3414.gif|600 px|thumb|centre|Figure 12: Endo Diels-Alder Reaction Profile]]
[[File:Chelotropic_Reaction_Profile_cm3414.gif|600 px|thumb|centre|Figure 13: Chelotropic Reaction Profile]]

This shows that the preferred reaction route (provided the reaction is irreversible) is the endo Diels-Alder reaction, since reaction has the lowest activation energy (this is the kinetic product). The exo Diels-Alder reaction produces product which is thermodynamically more stable than the endo, however the product of the chelotropic reaction is lowest in energy and therefore the most thermodynamically stable.