ChemWiki - User contributions [en]

Rep:MOD:Ard16MO lab

2018-05-18T16:58:34Z

Ard16: /* Molecular Orbitals */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

'''B3LYP/6-31G level(d.p.)'''
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER2_BASIS_DONE2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_MONOMER_BASIS_DONE1.LOG</uploadedFileContents>
</jmolApplet></jmol>
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol, and this energy difference would be the dissociation energy. A dissociation energy of +95kj/mol reflects the fact that there are two extra covalent bonds in the dimer which must be broken for it to dissociate.

However the energy difference is much weaker than the strength of two Al-Cl bonds. This is because the monomer displays unusual stability. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. The right orientation comes from the fact the molecule is planar. Electron density from the halogens feeds into the empty p orbital relieving the Alumnium electron deficiency. However this interaction is not as strong as a covalent bond, rendering the formation of the dimer more favourable.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn. The dominant interactions across the MOs were p orbital interaction, occuring by far the most. P orbital interacytions are less strong than s interactions, but stronger than d orbital interactions. p orbital interactions are stronger when end-on as oppose to side-on as end-on generates greater overlap, as these interactions are more directed, making it a sigma like interactions as oppose to a pi type.

1
This bonding MO comes from p orbitals on all atoms.
[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
2
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
3
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:57:56Z

Ard16: /* Energy Discussion */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

'''B3LYP/6-31G level(d.p.)'''
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER2_BASIS_DONE2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_MONOMER_BASIS_DONE1.LOG</uploadedFileContents>
</jmolApplet></jmol>
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol, and this energy difference would be the dissociation energy. A dissociation energy of +95kj/mol reflects the fact that there are two extra covalent bonds in the dimer which must be broken for it to dissociate.

However the energy difference is much weaker than the strength of two Al-Cl bonds. This is because the monomer displays unusual stability. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. The right orientation comes from the fact the molecule is planar. Electron density from the halogens feeds into the empty p orbital relieving the Alumnium electron deficiency. However this interaction is not as strong as a covalent bond, rendering the formation of the dimer more favourable.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn. The dominant interactions across the MOs were p orbital interaction, occuring by far the most. P orbital interacytions are less strong than s interactions, but stronger than d orbital interactions. p orbital interactions are stronger when end-on as oppose to side-on as end-on generates greater overlap, as these interactions are more directed, making it a sigma like interactions as oppose to a pi type.
The electronegatitvity difference between Al and Cl and Br is large, with chlorine and bromine being much more electronegative. This

1
This bonding MO comes from p orbitals on all atoms.
[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
2
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
3
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:54:04Z

Ard16: /* B3LYP/6-31G level(d.p.) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

'''B3LYP/6-31G level(d.p.)'''
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER2_BASIS_DONE2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_MONOMER_BASIS_DONE1.LOG</uploadedFileContents>
</jmolApplet></jmol>
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable.

However the energy difference is much weaker than the strength of two Al-Cl bonds. This is because the monomer displays unusual stability. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Electron density from the halogens feeds into the empty p orbital relieving the Alumnium electron deficiency. However this interaction is not as strong as a covalent bond, rendering the formation of the dimer more favourable.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn. The dominant interactions across the MOs were p orbital interaction, occuring by far the most. P orbital interacytions are less strong than s interactions, but stronger than d orbital interactions. p orbital interactions are stronger when end-on as oppose to side-on as end-on generates greater overlap, as these interactions are more directed, making it a sigma like interactions as oppose to a pi type.
The electronegatitvity difference between Al and Cl and Br is large, with chlorine and bromine being much more electronegative. This

1
This bonding MO comes from p orbitals on all atoms.
[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
2
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
3
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:47:00Z

Ard16: /* Molecular Orbitals */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER2_BASIS_DONE2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_MONOMER_BASIS_DONE1.LOG</uploadedFileContents>
</jmolApplet></jmol>
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable.

However the energy difference is much weaker than the strength of two Al-Cl bonds. This is because the monomer displays unusual stability. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Electron density from the halogens feeds into the empty p orbital relieving the Alumnium electron deficiency. However this interaction is not as strong as a covalent bond, rendering the formation of the dimer more favourable.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn. The dominant interactions across the MOs were p orbital interaction, occuring by far the most. P orbital interacytions are less strong than s interactions, but stronger than d orbital interactions. p orbital interactions are stronger when end-on as oppose to side-on as end-on generates greater overlap, as these interactions are more directed, making it a sigma like interactions as oppose to a pi type.
The electronegatitvity difference between Al and Cl and Br is large, with chlorine and bromine being much more electronegative. This

1
This bonding MO comes from p orbitals on all atoms.
[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
2
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
3
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:36:55Z

Ard16: /* Molecular Orbitals */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER2_BASIS_DONE2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_MONOMER_BASIS_DONE1.LOG</uploadedFileContents>
</jmolApplet></jmol>
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable.

However the energy difference is much weaker than the strength of two Al-Cl bonds. This is because the monomer displays unusual stability. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Electron density from the halogens feeds into the empty p orbital relieving the Alumnium electron deficiency. However this interaction is not as strong as a covalent bond, rendering the formation of the dimer more favourable.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn. The dominant interactions across the MOs were p orbital interaction, occuring by far the most. P orbital interacytions are less strong than s interactions, but stronger than d orbital interactions. p orbital interactions are stronger when end-on as oppose to side-on as end-on generates greater overlap, making it a sigma like interactions as oppose to a pi type.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:31:55Z

Ard16: /* Energy Discussion */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER2_BASIS_DONE2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_MONOMER_BASIS_DONE1.LOG</uploadedFileContents>
</jmolApplet></jmol>
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable.

However the energy difference is much weaker than the strength of two Al-Cl bonds. This is because the monomer displays unusual stability. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Electron density from the halogens feeds into the empty p orbital relieving the Alumnium electron deficiency. However this interaction is not as strong as a covalent bond, rendering the formation of the dimer more favourable.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:28:55Z

Ard16: /* AlCl2Br */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER2_BASIS_DONE2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_MONOMER_BASIS_DONE1.LOG</uploadedFileContents>
</jmolApplet></jmol>
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:27:55Z

Ard16: /* Isomer b (Trans terminal Br) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER2_BASIS_DONE2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:27:19Z

Ard16: /* Isomer e (bridging BRs) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ATRD16_ISOMER5_GEN4_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:26:50Z

Ard16: /* BBr3 */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_INPUT2.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:26:09Z

Ard16: /* BBr3 */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==

Method, basis set; B3LYP/6-31G(d,p)LANL2DZ
[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:25:24Z

Ard16: /* Ammonia Borane */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_ADDUCT_FREQ1.LOG</uploadedFileContents>
</jmolApplet></jmol>
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:24:59Z

Ard16: /* NH3 */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:24:17Z

Ard16: /* NH3 */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Media:ARD16_NH3_FREQ</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:24:02Z

Ard16: /* NH3 */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Media:ARD16_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:22:08Z

Ard16: /* B3LYP/6-31G level(d.p.) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
<jmol><jmolApplet>
<title>Optimised BH3 Molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ARD16_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:21:07Z

Ard16: /* Molecular Orbitals */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

Rep:MOD:Ard16MO lab

2018-05-18T16:20:45Z

Ard16: /* Molecular Orbitals */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -2352.38027 Hartree, compared to 2352.406308 Hartree for isomer B. The isolated monomers are therefore less stable than the dimer. The energy difference is 0.03601 Hartree or 95kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

===Molecular Orbitals===
The MOs from the trans terminal Br isomer, Isomer b were visualised and drawn.

[[File:Ard16-MO40.jpg|none|thumb|685x750px|MO-40, a strongly bonding orbital]]
[[File:Ard16_HOMO.jpg|none|thumb|685x750px|MO-54, a mixed interaction orbital, overall antibondingl]]
[[File:File:Ard16 MO45.jpg|none|thumb|685x750px|MO-45, an anti-bonding orbital]]

=References=

File:Ard16 HOMO.jpg

2018-05-18T16:19:10Z

Ard16:

Rep:MOD:Ard16MO lab

2018-05-18T16:16:57Z

Ard16: /* Molecular Orbitals */

Rep:MOD:Ard16MO lab

2018-05-18T16:15:21Z

Ard16: /* BH3 */

Rep:MOD:Ard16MO lab

2018-05-18T16:14:17Z

Ard16: /* Molecular Orbitals */

Rep:MOD:Ard16MO lab

2018-05-18T16:13:48Z

Ard16: /* Energy Discussion */

File:Ard16-MO40.jpg

2018-05-18T16:13:11Z

Ard16:

File:Ard16 MO54.jpg

2018-05-18T16:12:53Z

Ard16:

File:Ard16 MO45.jpg

2018-05-18T16:12:39Z

Ard16:

Rep:MOD:Ard16MO lab

2018-05-18T14:46:31Z

Ard16: /* Energy Discussion */

Rep:MOD:Ard16MO lab

2018-05-18T14:45:47Z

Ard16: /* Energy Discussion */

Rep:MOD:Ard16MO lab

2018-05-18T14:40:53Z

Ard16: /* AlCl2Br */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER_BASIS_DONE1.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

File:ARD16 MONOMER BASIS DONE1.LOG

2018-05-18T14:40:39Z

Ard16:

Rep:MOD:Ard16MO lab

2018-05-18T14:40:26Z

Ard16: /* AlCl2Br */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

File:Ard16 monomer summary.PNG

2018-05-18T14:40:12Z

Ard16:

Rep:MOD:Ard16MO lab

2018-05-18T14:39:55Z

Ard16: /* AlCl2Br */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.4227 -0.0030 -0.0024 -0.0022 2.8334 2.9165
Low frequencies --- 120.5196 133.8366 185.7806

</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

Rep:MOD:Ard16MO lab

2018-05-18T14:38:45Z

Ard16: /* AlCl2Br */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000004 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>

=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

Rep:MOD:Ard16MO lab

2018-05-18T14:34:24Z

Ard16: /* Discussion */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.00998 hartree or 26Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

Rep:MOD:Ard16MO lab

2018-05-18T14:29:25Z

Ard16: /* Isomer b (Trans terminal Br) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

Rep:MOD:Ard16MO lab

2018-05-18T14:29:14Z

Ard16: /* Isomer e (bridging BRs) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary1.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

File:Ar16 trans opt summary1.PNG

2018-05-18T14:29:04Z

Ard16:

File:Ard16 bridge isomer summary1.PNG

2018-05-18T14:28:31Z

Ard16:

Rep:MOD:Ard16MO lab

2018-05-18T14:27:09Z

Ard16: /* Isomer e (bridging BRs) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER5_GEN4_FREQ1.LOG| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

File:ATRD16 ISOMER5 GEN4 FREQ1.LOG

2018-05-18T14:26:52Z

Ard16:

File:Ard16 bridge isomer summary.PNG

2018-05-18T14:26:34Z

Ard16: Ard16 uploaded a new version of File:Ard16 bridge isomer summary.PNG

Rep:MOD:Ard16MO lab

2018-05-18T14:25:15Z

Ard16: /* Isomer e (bridging BRs) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16 ISOMER5 OPT D3H 1 FREQ1.txt| Here]] for a link to the frequency log file.

<pre>Low frequencies --- -5.1161 -4.9835 -3.1302 -0.0027 0.0013 0.0020
Low frequencies --- 14.8567 63.2780 86.0772
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

Rep:MOD:Ard16MO lab

2018-05-18T14:24:10Z

Ard16: /* Isomer e (bridging BRs) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

Click [[Media:ATRD16 ISOMER5 OPT D3H 1 FREQ1.txt| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0003 0.0000 0.0000 1.4709 2.4526 3.9729
Low frequencies --- 16.9907 52.6197 73.0938
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

Rep:MOD:Ard16MO lab

2018-05-18T14:09:46Z

Ard16: /* Isomer b (Trans terminal Br) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.001190 0.001800 YES
RMS Displacement 0.000543 0.001200 YES
</pre>

Click [[Media:ATRD16 ISOMER5 OPT D3H 1 FREQ1.txt| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0003 0.0000 0.0000 1.4709 2.4526 3.9729
Low frequencies --- 16.9907 52.6197 73.0938
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

Rep:MOD:Ard16MO lab

2018-05-18T14:08:50Z

Ard16: /* Isomer b (Trans terminal Br) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.001190 0.001800 YES
RMS Displacement 0.000543 0.001200 YES
</pre>

Click [[Media:ATRD16 ISOMER5 OPT D3H 1 FREQ1.txt| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0003 0.0000 0.0000 1.4709 2.4526 3.9729
Low frequencies --- 16.9907 52.6197 73.0938
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_BASIS_DONE2| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

File:ATRD16 ISOMER2 BASIS DONE2.LOG

2018-05-18T14:08:41Z

Ard16:

File:Ar16 trans opt summary.PNG

2018-05-18T14:07:01Z

Ard16: Ard16 uploaded a new version of File:Ar16 trans opt summary.PNG

Rep:MOD:Ard16MO lab

2018-05-18T14:06:41Z

Ard16: /* Isomer b (Trans terminal Br) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.001190 0.001800 YES
RMS Displacement 0.000543 0.001200 YES
</pre>

Click [[Media:ATRD16 ISOMER5 OPT D3H 1 FREQ1.txt| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0003 0.0000 0.0000 1.4709 2.4526 3.9729
Low frequencies --- 16.9907 52.6197 73.0938
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000023 0.000300 YES
Maximum Displacement 0.001323 0.001800 YES
RMS Displacement 0.000435 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_OPT_C2H_FREQs.txt| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.7684 -2.2995 -0.0041 -0.0030 -0.0024 0.8521
Low frequencies --- 17.7338 49.0103 72.9394

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=

Rep:MOD:Ard16MO lab

2018-05-18T14:04:41Z

Ard16: /* Isomer b (Trans terminal Br) */

== Molecular Orbital Lab- Arun Dolan ==

=== General MO Calculations ===

== BH3 ==

====== '''B3LYP/6-31G level(d.p.)''' ======
[[File:Ard16 mo report-bh3 optm table.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000042 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

Click [[Media:ARD16_BH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

====== Frequency Table ======
{| class="wikitable"
!Mode
!Vibrational Frequency/cm-1
!Intensity/au
!IR active?
!Type
!Symmetry
|-
|1
|1163
|93
|YES
|Out-of-plane bend
|A2"
|-
|2
|1213
|14
|slight
|bend
|E'
|-
|3
|1213
|14
|slight
|bend
|E'
|-
|4
|2582
|0
|NO
|Symmetric Stretch
|A1'
|-
|5
|2716
|126
|YES
|Assymetric Strech
|E'
|-
|6
|2716
|126
|YES
|Assymetric Strech
|E'
|}

There a six vibrations however only three in the above spectra. The reason for this is that two of the vibrations, the assymetric stretches and the bends, are degenerate and so are only seen once. The remaining missing 'vibration' is the symmetric stretch. This vibration is not IR active as the molecule's dipole does not change upon vibration.

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

[[File:Ard16_mo_report_spectrumBH3.PNG|thumb|BH3 IR spectrum.|none|428x428px]]

===MO Discussion===
[[File:Ard16 MOs Bh3.PNG|none|thumb|581x581px|Mo Diagram of BH3]]Diagram taken from Hunt Research Group website<ref>HuntResearchGroup, <nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed
</nowiki>17th May 2018).</ref>
The MOs from the LCAO approximation and the real computed MOs resemble each other but are not identical. One of the major differences is that electron density is centered around the atoms in a LCAO approach, for example MO a1'. However the real MO presents a smear of electron density which is not restricted to the atoms . The e' MOs are another example of this, rather than representing p and s orbitals as in the LCAO the electron density in reality is spread over the atoms in a more fluid manner. Furthermore the a1' lUMO MO looks markedly different from the filled MOs, suggesting anti-bonding orbitals may differ from the LCAO approximation more than MOs. The co-efficents of the hydrogens are much larger than in the LCAO picture, bringing more electron density away from the center of the molecule and bonding areas.

The differences show that the LCAO is a good approximation for the bonding orbitals. The localisation of electron density around atoms in the LCAO approximation does limit its accuracy for visualising MOs, however for easily predicting the different MOs, and possible inetracting MOs between molecules LCAO is suitable. However as above the LUMO the LCAO approximation becomes less accurate as anti-bonding orbitals deviate more strongly from the LCAO picture, it becomes an unsuitable mechanism for visualising MOs. However as most reactions between molecules are concerned with the LUMO and bonding orbitals the usefullness of the LCAO approximation is not too badly affected.

===Ammonia Borane Reaction===
====NH3====
Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_NH3_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES </pre>

Click [[Media:ARD16_NH3_FREQ.LOG| here]] for the frequency file

<pre>Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865 </pre>

====Ammonia Borane====

Method: RB3LYP Basis Set: 6-31G(d,p)
[[File:Ard16_adduct_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000570 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
</pre>

Click [[Media:ARD16_ADDUCT_FREQ1.LOG|here]] for the frequency file

<pre>Low frequencies --- -0.0576 -0.0501 -0.0074 21.6263 21.6362 40.3340
Low frequencies --- 265.9844 632.3694 640.1233
</pre>

==== Reaction ====
For the reaction NH3 + BH3 => NH3BH3 

Energies in Hartree unless stated

E(NH3)=-56.55777

E(BH3)=-26.61533

E(NH3BH3)=-83.22469

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE=-0.051594

ΔE=135Kj/mol
<nowiki> </nowiki>This result compares relatively well with computational literature suggesting the B-N bond in ammonia borane is 184Kj/mol<ref>Dreux et al, 2017, J. Phys. Chem. A 121, 31, 5884-5893</ref>.

An N-B dative covalent bond strength of 135kJ/mol can be compared to the B-B bond strength is 293 Kj/mol, and the N-N is 167 Kj/mol single bond strengths for context. The N-N single bond strength is known to be weak due to repulsive lone pair interactions. The N-B bond is of similar strength so can also be deemed weak, especially given that it is substantially weaker than the B-B bond strength.

== BBr3 ==
Method, basis set; B3LYP/6-31G(d,p)LANL2DZ[[File:ARD16_bBR3-SUMMARY.PNG|none|thumb|381x381px|Summary Table]]

<pre>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
</pre>

Click [[Media:ARD16_INPUT2.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -2.3428 -0.0035 -0.0018 0.0762 0.6278 0.6278
Low frequencies --- 155.9407 155.9410 267.6924
</pre>

D-space link: The frequency analysis would not run on the server. Neither myself nor the demonstrators could work out why. I therefore ran the calculation on my local machine, and so there frequency calculation has not been published. I there include a link instead to the published optimisation file. {{DOI|10042/202405}}

== Project Section ==

===Main Group Halides===

====== Isomers of Al2Br2Cl4 ======
{| class="wikitable"
!Isomer label
!Structure
!Symmetry
|-
|a
|[[File:Ard16 isomer1.PNG|thumb]]
|C2V
|-
|b
|[[File:Ard16 isomer 2.PNG|thumb]]
|C2h
|-
|c
|[[File:Ard16 isomer5.PNG|thumb]]
|C2V
|-
|d
|[[File:Ard16 isomer4.PNG|thumb]]
|C1
|-
|e
|[[File:Ard16 isomer3.PNG|thumb]]
|D2h
|}

===Energies of Isomers ===
==== Isomer e (bridging BRs)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ard16_bridge_isomer_summary.PNG|none|thumb|381x381px|Summary Table]]

<pre>Item Value Threshold Converged?
Maximum Force 0.000102 0.000450 YES
RMS Force 0.000047 0.000300 YES
Maximum Displacement 0.001190 0.001800 YES
RMS Displacement 0.000543 0.001200 YES
</pre>

Click [[Media:ATRD16 ISOMER5 OPT D3H 1 FREQ1.txt| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0003 0.0000 0.0000 1.4709 2.4526 3.9729
Low frequencies --- 16.9907 52.6197 73.0938
</pre>

====Isomer b (Trans terminal Br)====
Method, Basis set: B3LYP/6-31G(d,p)LANL2DZ
[[File:Ar16 trans opt summary.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000244 0.001800 YES
RMS Displacement 0.000092 0.001200 YES
</pre>

Click [[Media:ATRD16_ISOMER2_OPT_C2H_FREQs.txt| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -3.9781 -0.0003 0.0000 0.0000 1.2549 2.4981
Low frequencies --- 17.8636 40.4366 64.5554

</pre>

====Discussion====
Out of Isomer E and isomer B, Isomer B with the trans terminal bromine is more stable by 0.01052 hartree or 28Kj/mol. The extra stability can be explained by examining the bonds in each structure. In each case the bridging atom forms a dative covalent bond to an alumnium atom explaining the odd halogen valency. Therefore the two structures both have four Al-Cl bonds, two Al-Br bonds and then two extra dative Br-Al bonds when the bromines are bridging compared to two extra Cl-Al bonds when the chlorines are bridging. The literature bond strengths are 502Kj/mol for Al-Cl and 429Kj/mol for Al-Br<ref>Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007</ref>. The Al-Cl bond is therefore stronger, explaining the relative stability when the chlorine atoms are bridging.

The increased strength of the Al-Cl bond when compared to the Al-Br bond can be rationalised given that Al and Cl are both in the third row of the periodic table, but Br is in row four. Therefore bromine's orbitals are likely to be more diffuse when compared to aluminium's. The overlap is therefore less good when compared to chlorine's more contracted orbitals. The interaction between Al and Cl are between 3p and 3p compared to 4p and 3p for Al and Br. A lower overlap integral leads to a lower interaction energy.

===== Dissociation =====

====== AlCl2Br ======
method:RB3YP, Basis Set:PP LANL2DZ
[[File:Ard16_monomer.PNG|none|thumb|381x381px|Summary Table]]

<pre> Item Value Threshold Converged?
Maximum Force 0.000150 0.000450 YES
RMS Force 0.000080 0.000300 YES
Maximum Displacement 0.001191 0.001800 YES
RMS Displacement 0.000750 0.001200 YES

</pre>

Click [[Media:ARD16_MONOMER1_FREQ.LOG| Here]] for a link to the frequency log file.

<pre> Low frequencies --- -0.0001 0.0000 0.0000 3.7125 5.1765 6.2784
Low frequencies --- 108.1083 119.9091 168.6294
</pre>
=====Energy Discussion=====
The energy for two isolated monomers is -90.43799 Hartree, compared to -90.47288 for isomer E. The isolated monomers are therefore less stable than the dimer. The energy difference is around 91kj/mol. The two extra covalent bonds in the dimer provide extra stability, and so it is expected that the dimer would be more stable. However the energy difference is much weaker than the strength of two Al-Cl bonds. The extra stability of the monomer comes from the empty Al p orbital having the right orientation to interaction with lone pairs on the surrounding halogen atoms on the same molecule. Therefore greater stability is attained. However these interactions are side-on, whereas the empty Al lone pair in a dimer has more end-on character granting it extra stability.

=References=