ChemWiki - User contributions [en]

Rep:Mod:CH1516

2018-05-18T15:30:01Z

Ch1516: /* about this wiki */

== about energy ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N.

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0028 0.0031 0.0038 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers. The dimerisation brings down the energy of the whole system.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|1000px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|1000px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|1000px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

[2]ː Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007.

Rep:Mod:CH1516

2018-05-18T15:29:15Z

Ch1516: /* MOs of isomer C */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N.

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0028 0.0031 0.0038 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers. The dimerisation brings down the energy of the whole system.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|1000px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|1000px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|1000px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

[2]ː Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007.

Rep:Mod:CH1516

2018-05-18T15:28:50Z

Ch1516: /* MOs of isomer C */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N.

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0028 0.0031 0.0038 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers. The dimerisation brings down the energy of the whole system.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|800px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|800px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|800px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

[2]ː Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007.

Rep:Mod:CH1516

2018-05-18T15:27:48Z

Ch1516: /* dissociation reaction */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N.

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0028 0.0031 0.0038 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers. The dimerisation brings down the energy of the whole system.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

[2]ː Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007.

Rep:Mod:CH1516

2018-05-18T15:21:40Z

Ch1516: /* low frequencies */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N.

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0028 0.0031 0.0038 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

[2]ː Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007.

Rep:Mod:CH1516

2018-05-18T15:15:17Z

Ch1516: /* reference */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N.

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

[2]ː Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007.

Rep:Mod:CH1516

2018-05-18T15:15:06Z

Ch1516: /* reference */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N.

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007.

Rep:Mod:CH1516

2018-05-18T15:14:56Z

Ch1516: /* energy calculation[2] */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N.

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:14:41Z

Ch1516: /* energy calculation */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation[2] ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2] This weak strength is because it's a dative bond, with two electrons from N

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:09:07Z

Ch1516: /* reference */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2]

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:07:10Z

Ch1516: /* energy calculation */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol.[2]

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:04:14Z

Ch1516: /* Computational level and basis set */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:03:36Z

Ch1516: /* low frequencies */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5200 -8.4726 -0.0035 0.0335 0.1919 26.4074
Low frequencies --- 1089.7616 1694.1863 1694.1866

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:02:14Z

Ch1516: /* Computational level and basis set */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/6-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:01:50Z

Ch1516: /* MO diagram[1] */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2" MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:01:18Z

Ch1516: /* MO diagram[1] */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:01:06Z

Ch1516: /* MO diagram[1] */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2 '' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T15:00:38Z

Ch1516: /* MO diagram[1] */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T14:59:44Z

Ch1516: /* MO diagram */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram[1] ===

[[File:hcytriciamofinal.PNG|600px]]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T14:59:03Z

Ch1516: /* vibration table */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| out-of-plane bending
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| symmetric bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| asymmetric bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| asymmetric bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T14:56:17Z

Ch1516: /* vibration table */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A"|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T14:54:55Z

Ch1516: /* vibration spectrum */

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|600px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T14:53:53Z

Ch1516:

== about this wiki ==

The energy units are converted by 0.0004 a.u. = 1 kJ/mol

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T14:50:53Z

Ch1516: /* Summary table */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:BH33-21Gsum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

File:BH33-21Gsum.PNG

2018-05-18T14:50:27Z

Ch1516:

Rep:Mod:CH1516

2018-05-18T14:44:15Z

Ch1516: /* MOs of isomer C */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

MO 53ː strong antibonding

[[File:CMO53sub.PNG|600px]]

MO 42ː medium antibonding

[[File:CMO42sub.PNG|600px]]

MO 31ː medium bonding

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T14:43:24Z

Ch1516: /* MOs of isomer C */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

[[File:CMO53sub.PNG|600px]]

[[File:CMO42sub.PNG|600px]]

[[File:CMO31sub.PNG|600px]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-18T14:42:29Z

Ch1516: /* MOs of isomer C */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

[[File:CMO53sub.PNG]]

[[File:CMO42sub.PNG]]

[[File:CMO31sub.PNG]]

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

File:CMO53sub.PNG

2018-05-18T14:41:00Z

Ch1516:

File:CMO42sub.PNG

2018-05-18T14:40:48Z

Ch1516:

File:CMO31sub.PNG

2018-05-18T14:40:36Z

Ch1516:

Rep:Mod:CH1516

2018-05-17T20:13:58Z

Ch1516: /* mini-projectː Al2Cl4Br2 */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

=== MOs of isomer C ===

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:40:26Z

Ch1516: /* dissociation reaction */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -1176.19014 a.u. = -2940475 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = 2×E(AlCl2Br) - E(isomerC) = 2×(-2940475 kJ/mol) - (-5881041 kJ/mol) = +91 kJ/mol

The energy change from Al2Cl4Br2 to AlCl2Br is positive, therefore, Al2Cl4Br2 is more stable than the isolated monomers.

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:37:10Z

Ch1516: /* DSpace identifier */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202431}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -729.15824 a.u. = -1822896 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(isomerC) - 2×E(AlCl2Br) = -5881041 kJ/mol - 2×(-1822896 kJ/mol) = -2235249 kJ/mol

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:36:27Z

Ch1516: /* low frequencies */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- 0.0025 0.0034 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -729.15824 a.u. = -1822896 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(isomerC) - 2×E(AlCl2Br) = -5881041 kJ/mol - 2×(-1822896 kJ/mol) = -2235249 kJ/mol

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:35:51Z

Ch1516: /* Item table */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -729.15824 a.u. = -1822896 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(isomerC) - 2×E(AlCl2Br) = -5881041 kJ/mol - 2×(-1822896 kJ/mol) = -2235249 kJ/mol

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:35:16Z

Ch1516: /* total energy */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-1176.19014 a.u.

-2940475 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -729.15824 a.u. = -1822896 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(isomerC) - 2×E(AlCl2Br) = -5881041 kJ/mol - 2×(-1822896 kJ/mol) = -2235249 kJ/mol

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:33:29Z

Ch1516: /* Summary table */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2be.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -729.15824 a.u. = -1822896 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(isomerC) - 2×E(AlCl2Br) = -5881041 kJ/mol - 2×(-1822896 kJ/mol) = -2235249 kJ/mol

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

File:ALCL2BRFREQ.LOG

2018-05-17T15:33:06Z

Ch1516: Ch1516 uploaded a new version of File:ALCL2BRFREQ.LOG

File:Alcl2be.PNG

2018-05-17T15:32:52Z

Ch1516:

Rep:Mod:CH1516

2018-05-17T15:17:38Z

Ch1516: /* dissociation reaction */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -729.15824 a.u. = -1822896 kJ/mol

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(isomerC) - 2×E(AlCl2Br) = -5881041 kJ/mol - 2×(-1822896 kJ/mol) = -2235249 kJ/mol

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:15:01Z

Ch1516: /* dissociation reaction */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer C, whose energy is -5881041 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(isomerC) - 2×E(AlCl2Br) = -5881041 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:14:22Z

Ch1516: /* relative stability of isomer A and isomer C */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 25 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer A, whose energy is -18673857 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(Al2Cl4Br2) - 2×E(AlCl2Br) = -18673857 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:13:52Z

Ch1516: /* relative stability of isomer A and isomer C */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer C is 14 kJ/mol lower than isomer A, hence more stable. This might be due to the fact that Al is in the same row as Cl, while Br is a row lower than Al. Therefore, there is a better orbital overlap between Al and Cl, which results in lower bond energy and greater stability.

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer A, whose energy is -18673857 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(Al2Cl4Br2) - 2×E(AlCl2Br) = -18673857 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:12:14Z

Ch1516: /* energies of isomers */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

Energy of isomer A

-2352.40631 a.u.

-5881016 kJ/mol

Energy of isomer C

-2352.41629 a.u.

-5881041 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer A is 14 kJ/mol lower than isomer C, hence more stable. This might be due to the fact that in isomer A the bridging atom is Br, while the bridging atom in isomer C is Cl. Br has a larger atomic radius than Cl. Therefore, in isomer A the central four-membered ring has less ring strain than isomer C, resulting in greater stability. However, my friend Ching-Ching Lam obtained the opposite result. This is probably due to the really small energy difference of the two isomers resulting in uncertainty

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer A, whose energy is -18673857 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(Al2Cl4Br2) - 2×E(AlCl2Br) = -18673857 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:11:35Z

Ch1516: /* 2 bridging Br ions */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

==== 2 bridging Br ions ====

-2352.40631 a.u.

-5881016 kJ/mol

==== the isomer with trans terminal Br and bridging Cl ions ====

-7469.53758 a.u.

-18673843 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer A is 14 kJ/mol lower than isomer C, hence more stable. This might be due to the fact that in isomer A the bridging atom is Br, while the bridging atom in isomer C is Cl. Br has a larger atomic radius than Cl. Therefore, in isomer A the central four-membered ring has less ring strain than isomer C, resulting in greater stability. However, my friend Ching-Ching Lam obtained the opposite result. This is probably due to the really small energy difference of the two isomers resulting in uncertainty

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer A, whose energy is -18673857 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(Al2Cl4Br2) - 2×E(AlCl2Br) = -18673857 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:10:58Z

Ch1516: /* DSpace identifier */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202428}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

==== 2 bridging Br ions ====

-7469.54265 a.u.

-18673857 kJ/mol

==== the isomer with trans terminal Br and bridging Cl ions ====

-7469.53758 a.u.

-18673843 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer A is 14 kJ/mol lower than isomer C, hence more stable. This might be due to the fact that in isomer A the bridging atom is Br, while the bridging atom in isomer C is Cl. Br has a larger atomic radius than Cl. Therefore, in isomer A the central four-membered ring has less ring strain than isomer C, resulting in greater stability. However, my friend Ching-Ching Lam obtained the opposite result. This is probably due to the really small energy difference of the two isomers resulting in uncertainty

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer A, whose energy is -18673857 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(Al2Cl4Br2) - 2×E(AlCl2Br) = -18673857 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:10:27Z

Ch1516: /* jmol image */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerC</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMCFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202408}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

==== 2 bridging Br ions ====

-7469.54265 a.u.

-18673857 kJ/mol

==== the isomer with trans terminal Br and bridging Cl ions ====

-7469.53758 a.u.

-18673843 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer A is 14 kJ/mol lower than isomer C, hence more stable. This might be due to the fact that in isomer A the bridging atom is Br, while the bridging atom in isomer C is Cl. Br has a larger atomic radius than Cl. Therefore, in isomer A the central four-membered ring has less ring strain than isomer C, resulting in greater stability. However, my friend Ching-Ching Lam obtained the opposite result. This is probably due to the really small energy difference of the two isomers resulting in uncertainty

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer A, whose energy is -18673857 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(Al2Cl4Br2) - 2×E(AlCl2Br) = -18673857 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:09:49Z

Ch1516: /* low frequencies */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.2179 -2.5716 0.0011 0.0018 0.0034 0.6119
Low frequencies --- 17.7000 48.9940 72.9499

==== jmol image ====

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202408}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

==== 2 bridging Br ions ====

-7469.54265 a.u.

-18673857 kJ/mol

==== the isomer with trans terminal Br and bridging Cl ions ====

-7469.53758 a.u.

-18673843 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer A is 14 kJ/mol lower than isomer C, hence more stable. This might be due to the fact that in isomer A the bridging atom is Br, while the bridging atom in isomer C is Cl. Br has a larger atomic radius than Cl. Therefore, in isomer A the central four-membered ring has less ring strain than isomer C, resulting in greater stability. However, my friend Ching-Ching Lam obtained the opposite result. This is probably due to the really small energy difference of the two isomers resulting in uncertainty

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer A, whose energy is -18673857 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(Al2Cl4Br2) - 2×E(AlCl2Br) = -18673857 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies

Rep:Mod:CH1516

2018-05-17T15:09:19Z

Ch1516: /* frequency analysis log file */

== BH3 3-21G ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES

== BH3 6-31G ==

=== computational level and basis set ===
B3LYP/6-31G level

=== summary table ===
[[File:hcybh3betteropt.PNG]]

=== total energy ===

-2352.40631 a.u.

-5881016 kJ/mol

=== item table ===
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_BH3_FREQ.LOG| HCY_BH3_FREQ.LOG]]

=== low frequencies lines ===
<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356

Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== vibration table ===

{| class="wikitable" border="1"
|+ vibration analysis
! mode # !! frequency(cm-1)!! intensity(arbitrary units) !! symmetry!! IR active?!! type
|-
| 1 || 1163|| 93|| A''|| yes|| angle deformation
|-
| 2 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 3 || 1213|| 14|| E'|| yes|| angle deformation
|-
| 4 || 2582|| 0|| A'|| no|| bond stretch
|-
| 5 || 2715|| 126|| E'|| yes|| bond stretch
|-
| 6 || 2715|| 126||E'|| yes|| bond stretch
|}

=== vibration spectrum ===

[[File:Bh3vibspec.PNG|300px]]

As we can see there is only three vibration peaks on the spectrum but six vibration modes in total. This is because vibration ̃no. 2 and vibration no. 3 are degenerate, they have the same vibration wavenumber so appear as a single peak. vibration no. 4 is IR inactive, because it is a symmetric bond stretch which gives no change in polarity, hence breaking the selection rule. Similarly, vibration no. 5 and no.6 are degenerate and appear as a single peak. Therefore, in total, only three peaks are shown.

=== MO diagram ===

[[File:hcytriciamofinal.PNG|600px]][1]

As we can see, the LCAO MOs give a good overall representation comparing to real MOs, especially for a1' and a2'' MOs. There is some small deviations for e' MOs, such as in the left LCAO MO, one hydrogen at the does not contribute to the MO at all, while in real MO there is some electron density from the bottom H.

It can be concluded that the qualitative MO gives a good representation of the real case with fair accuracy, what is more, the fact that LCAO MOs are really easy to generate enhance their usefulness overall.

== NH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

=== total energy ===

-56.55777 a.u.

-141394 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3_SYM_OPT.LOG| HCY_NH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -8.5646 -8.5588 -0.0041 0.0455 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Computational level and basis set ===
B3LYP/3-21G level

=== Summary table ===
[[File:hcynh3bh3summary.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

=== total energy ===

-83.22469 a.u.

-208062 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:HCY_NH3BH3_SYM_OPT.LOG| HCY_NH3BH3_SYM_OPT.LOG]]

=== low frequencies ===

Low frequencies --- -0.0614 -0.0457 -0.0067 21.7005 21.7064 40.6240
Low frequencies --- 266.0448 632.3709 640.1464

=== jmol image ===

<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>HCY_NH3BH3_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

=== energy calculation ===

E(NH3)=-56.55777 a.u.

E(BH3)=-26.61532 a.u.

E(NH3BH3)=-83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=(-83.22469)-[(-56.55777)+(-26.61532)] a.u.=-0.0516 a.u.=-129 kJ/mol

This is a weak bond, compared to B-N covalent bond. The latter is 377.9 kJ/mol

=== reference ===

== BBr3 ==

=== Computational level and basis set ===
B3LYP/Gen

=== Summary table ===
[[File:hcybbr3sum.PNG]]

=== Item table ===
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

=== total energy ===

-64.43645 a.u.

-161091 kJ/mol

=== frequency analysis log file ===

Frequency analysis log file [[Media:BBr3_freq.log| BBr3_freq.log]]

=== low frequencies ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== jmol image ===

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

=== DSpace identifier ===

{{DOI|10042/202408}}

== mini-projectː Al2Cl4Br2 ==

=== isomers and symmetries ===

[[File:hcyisma.PNG|300px]] symmetryː D2h

[[File:hcyismb.PNG|300px]] symmetryː C1

[[File:hismc.PNG|300px]] symmetryː C2h

[[File:hismd.PNG|300px]] symmetryː C2v

[[File:hisme.PNG|300px]] symmetryː C2v

=== isomer A ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismasum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000679 0.001800 YES
RMS Displacement 0.000339 0.001200 YES

==== total energy ====

-2352.40631 a.u.

-5881016 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMAFREQ.LOG| ISMAFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -5.1263 -5.0805 -3.1863 -0.0005 0.0028 0.0044
Low frequencies --- 14.8606 63.2610 86.0512

==== jmol image ====

<jmol><jmolApplet>
<title>optimised isomerA</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ISMAFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202429}}

=== isomer C ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:ismcsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000298 0.001200 YES

==== total energy ====

-2352.41629 a.u.

-5881041 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ISMCFREQ.LOG| ISMCFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

==== jmol image ====

<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>BBr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202408}}

=== AlCl2Br ===

==== Computational level and basis set ====
B3LYP/Gen

==== Summary table ====
[[File:alcl2brsum.PNG]]

==== Item table ====
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000064 0.000300 YES
Maximum Displacement 0.000524 0.001800 YES
RMS Displacement 0.000348 0.001200 YES

==== total energy ====

-729.15824 a.u.

-1822896 kJ/mol

==== frequency analysis log file ====

Frequency analysis log file [[Media:ALCL2BRFREQ.LOG| ALCL2BRFREQ.LOG]]

==== low frequencies ====

Low frequencies --- -4.5121 -3.5914 -1.7403 0.0018 0.0024 0.0025
Low frequencies --- 98.2863 117.8524 173.2027

==== jmol image ====

<jmol><jmolApplet>
<title>optimised AlCl2Br</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ALCL2BRFREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>̝

==== DSpace identifier ====

{{DOI|10042/202427}}

=== energies of isomers ===

==== 2 bridging Br ions ====

-7469.54265 a.u.

-18673857 kJ/mol

==== the isomer with trans terminal Br and bridging Cl ions ====

-7469.53758 a.u.

-18673843 kJ/mol

=== relative stability of isomer A and isomer C ===

The relative energy of isomer A is 14 kJ/mol lower than isomer C, hence more stable. This might be due to the fact that in isomer A the bridging atom is Br, while the bridging atom in isomer C is Cl. Br has a larger atomic radius than Cl. Therefore, in isomer A the central four-membered ring has less ring strain than isomer C, resulting in greater stability. However, my friend Ching-Ching Lam obtained the opposite result. This is probably due to the really small energy difference of the two isomers resulting in uncertainty

=== dissociation reaction ===

My stable isomer among the two isomer above is isomer A, whose energy is -18673857 kJ/mol.

The energy of AlCl2Br is -5846.26389 a.u. = -14615659 kJ/mol.

Therefore, the dissociation energy of Al2Cl4Br2 = ΔE = E(Al2Cl4Br2) - 2×E(AlCl2Br) = -18673857 kJ/mol - 2×-14615659 kJ/mol = 10557461

== reference ==

[1]ː LCAO MO diagram taken from Dr. P. Hunt http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf
[2]ː Y Luo, Bond Dissociation Energies