ChemWiki - User contributions [en]

File:Vssj umo4 Al2Cl4Br2 chemdraw.png

2019-05-24T12:46:35Z

Vsj17:

File:Vssj umo3 Al2Cl4Br2 chemdraw.png

2019-05-24T12:46:18Z

Vsj17:

File:Vssj umo2 Al2Cl4Br2 chemdraw.png

2019-05-24T12:45:59Z

Vsj17:

File:Vssj umo1 Al2Cl4Br2 chemdraw.png

2019-05-24T12:45:40Z

Vsj17:

ICL:1905

2019-05-24T12:45:23Z

Vsj17: /* Questions and answers - Al2Cl4Br2 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

=== Questions and answers - Al2Cl4Br2 ===

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs
|-
| [[File:vssj_lumo_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1 - LUMO.]] || [[File:vssj_lumo_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_umo1_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 2.]] || [[File:vssj_umo1_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_umo2_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 3.]] || [[File:vssj_umo2_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_umo3_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 4.]] || [[File:vssj_umo3_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_umo4_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 5.]] || [[File:vssj_umo4_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_homo_Al2Cl4Br2.png|400px|thumb|Occupied MO 1 - HOMO.]] || [[File:vssj_homo_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_omo1_Al2Cl4Br2.png|400px|thumb|Occupied MO 2.]] || [[File:vssj_omo1_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_omo2_Al2Cl4Br2.png|400px|thumb|Occupied MO 3.]] || [[File:vssj_omo2_Al2Cl4Br2_chemdraw.png|400px]]
|}

File:Vssj omo2 Al2Cl4Br2 chemdraw.png

2019-05-24T12:14:42Z

Vsj17:

File:Vssj omo1 Al2Cl4Br2 chemdraw.png

2019-05-24T12:14:24Z

Vsj17:

File:Vssj homo Al2Cl4Br2 chemdraw.png

2019-05-24T12:13:57Z

Vsj17:

File:Vssj lumo Al2Cl4Br2 chemdraw.png

2019-05-24T12:13:35Z

Vsj17:

ICL:1905

2019-05-24T12:12:58Z

Vsj17: /* Questions and answers - Al2Cl4Br2 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

=== Questions and answers - Al2Cl4Br2 ===

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs
|-
| [[File:vssj_lumo_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1 - LUMO.]] || [[File:vssj_lumo_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_umo1_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 2.]] || cell
|-
| [[File:vssj_umo2_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 3.]] || cell
|-
| [[File:vssj_umo3_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 4.]] || cell
|-
| [[File:vssj_umo4_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 5.]] || cell
|-
| [[File:vssj_homo_Al2Cl4Br2.png|400px|thumb|Occupied MO 1 - HOMO.]] || [[File:vssj_homo_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_omo1_Al2Cl4Br2.png|400px|thumb|Occupied MO 2.]] || [[File:vssj_omo1_Al2Cl4Br2_chemdraw.png|400px]]
|-
| [[File:vssj_omo2_Al2Cl4Br2.png|400px|thumb|Occupied MO 3.]] || [[File:vssj_omo2_Al2Cl4Br2_chemdraw.png|400px]]
|}

File:Vssj omo2 Al2Cl4Br2.png

2019-05-24T11:41:47Z

Vsj17:

File:Vssj omo1 Al2Cl4Br2.png

2019-05-24T11:41:27Z

Vsj17:

File:Vssj umo4 Al2Cl4Br2.png

2019-05-24T11:40:56Z

Vsj17:

File:Vssj umo3 Al2Cl4Br2.png

2019-05-24T11:40:30Z

Vsj17:

File:Vssj umo2 Al2Cl4Br2.png

2019-05-24T11:39:59Z

Vsj17:

ICL:1905

2019-05-24T11:39:32Z

Vsj17: /* Questions and answers - Al2Cl4Br2 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

=== Questions and answers - Al2Cl4Br2 ===

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs + explanation
|-
| [[File:vssj_lumo_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1 - LUMO.]] || cell
|-
| [[File:vssj_umo1_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 2.]] || cell
|-
| [[File:vssj_umo2_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 3.]] || cell
|-
| [[File:vssj_umo3_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 4.]] || cell
|-
| [[File:vssj_umo4_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 5.]] || cell
|-
| [[File:vssj_homo_Al2Cl4Br2.png|400px|thumb|Occupied MO 1 - HOMO.]] || cell
|-
| [[File:vssj_omo1_Al2Cl4Br2.png|400px|thumb|Occupied MO 2.]] || cell
|-
| [[File:vssj_omo2_Al2Cl4Br2.png|400px|thumb|Occupied MO 3.]] || cell
|}

ICL:1905

2019-05-24T11:37:33Z

Vsj17: /* Questions and answers - Al2Cl4Br2 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

=== Questions and answers - Al2Cl4Br2 ===

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs + explanation
|-
| [[File:vssj_lumo_Al2Cl4Br2.png|400px|thumb|LUMO.]] || cell
|-
| [[File:vssj_umo1_Al2Cl4Br2.png|400px|thumb|HOMO.]] || cell
|-
| [[File:vssj_umo2_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1.]] || cell
|-
| [[File:vssj_umo3_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1.]] || cell
|-
| [[File:vssj_umo4_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1.]] || cell
|-
| [[File:vssj_homo_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1.]] || cell
|-
| [[File:vssj_omo1_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1.]] || cell
|-
| [[File:vssj_omo2_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1.]] || cell
|}

ICL:1905

2019-05-24T11:29:37Z

Vsj17: /* Questions and answers - Al2Cl4Br2 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

=== Questions and answers - Al2Cl4Br2 ===

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs !! heading !! heading !! heading
|-
| [[File:vssj_lumo_Al2Cl4Br2.png|400px|thumb|LUMO.]] || cell || cell || cell || cell
|-
| [[File:vssj_homo_Al2Cl4Br2.png|400px|thumb|HOMO.]] || cell || cell || cell || cell
|-
| [[File:vssj_umo1_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1.]] || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|}

File:Vssj umo1 Al2Cl4Br2.png

2019-05-24T11:22:15Z

Vsj17:

ICL:1905

2019-05-24T11:22:02Z

Vsj17: /* Questions and answers - Al2Cl4Br2 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

=== Questions and answers - Al2Cl4Br2 ===

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs !! heading !! heading !! heading
|-
| [[File:vssj_lumo_Al2Cl4Br2.png|400px|thumb|LUMO.]] || cell || cell || cell || cell
|-
| [[File:vssj_homo_Al2Cl4Br2.png|400px|thumb|HOMO.]] || cell || cell || cell || cell
|-
| [[File:vssj_umo1_Al2Cl4Br2.png|400px|thumb|Unoccupied MO 1.]] || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|}

File:Vssj homo Al2Cl4Br2.png

2019-05-24T11:19:09Z

Vsj17:

ICL:1905

2019-05-24T11:18:55Z

Vsj17: /* Al2Cl4Br2 where Br atoms are bridging Al atoms together */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

=== Questions and answers - Al2Cl4Br2 ===

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs !! heading !! heading !! heading
|-
| [[File:vssj_lumo_Al2Cl4Br2.png|400px|thumb|LUMO.]] || cell || cell || cell || cell
|-
| [[File:vssj_homo_Al2Cl4Br2.png|400px|thumb|HOMO.]] || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|}

File:Vssj lumo Al2Cl4Br2.png

2019-05-24T11:16:20Z

Vsj17:

ICL:1905

2019-05-24T11:15:41Z

Vsj17: /* Al2Cl4Br2 where Br atoms are bridging Al atoms together */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs !! heading !! heading !! heading
|-
| [[File:vssj_lumo_Al2Cl4Br2.png|400px|thumb|LUMO.]] || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|}

ICL:1905

2019-05-24T11:11:24Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

{| class="wikitable" border="1"
! Real MO !! LCAOs !! heading !! heading !! heading
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|-
| cell || cell || cell || cell || cell
|}

ICL:1905

2019-05-24T10:52:26Z

Vsj17: /* Al2Cl4Br2 where Br atoms are bridging Al atoms together */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-24T10:51:19Z

Vsj17: /* Al2Cl4Br2 where Br atoms are bridging Al atoms together */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

<pre>
2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.
</pre>

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

<pre>
4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.
</pre>

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

The dimer, i.e. Al2Cl4Br2, is more stable than the isolated monomer, i.e. AlCl2Br. Dimerisation occurs in order to reduce the electron deficiency seen in Al. It is also because the 3p-3p π orbital overlap (between Al and Cl) is not good in AlCl2Br, and greater orbital overlap is seen in the dimer, hence making it more stable.

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-24T10:34:48Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

<pre>
2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.
</pre>

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

<pre>
4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer
where Br atoms are bridging is less stable than those where Cl atoms are bridging.
</pre>

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

<pre>
6. Is the product more or less stable than the isolated monomers?
</pre>

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-24T10:33:54Z

Vsj17: /* Al2Cl4Br2 where Br atoms are bridging Al atoms together */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

<pre>
2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.
</pre>

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

<pre>
4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.
</pre>

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

<pre>
6. Is the product more or less stable than the isolated monomers?
</pre>

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-24T10:32:56Z

Vsj17: /* Al2Cl4Br2 where Br atoms are bridging Al atoms together */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

<pre>
2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.
</pre>

<pre>
3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.
</pre>

<pre>
4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.
</pre>

<pre>
5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1
</pre>

<pre>
6. Is the product more or less stable than the isolated monomers?
</pre>

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-24T10:32:02Z

Vsj17: /* Al2Cl4Br2 where Br atoms are bridging Al atoms together */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

<pre>
2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.
</pre>

<pre>
3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.
</pre>

<pre>
4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.
</pre>

<pre>
5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1
</pre>

<pre>
6. Is the product more or less stable than the isolated monomers?
</pre>

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-24T10:18:56Z

Vsj17: /* Al2Cl4Br2 where Br atoms are bridging Al atoms together */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = Cs.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-24T10:01:57Z

Vsj17: /* Molecular Orbital Diagram of BH3 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-24T10:01:45Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

File:Vssj antibonding1 bh3.png

2019-05-23T17:03:26Z

Vsj17:

ICL:1905

2019-05-23T17:02:51Z

Vsj17: /* Molecular Orbital Diagram of BH3 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

[[File:vssj_antibonding1_bh3.png|center|400px|thumb|This MO is an accurate portrayal of one of the antibonding orbitals in BH3 (2e' MO - where the p orbital is vertical).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

File:Vssj HOMO2 BH3.png

2019-05-23T16:57:28Z

Vsj17:

ICL:1905

2019-05-23T16:57:15Z

Vsj17: /* Molecular Orbital Diagram of BH3 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

[[File:vssj_HOMO2_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is horizontal).]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-23T16:56:43Z

Vsj17: /* BH3 IR Spectrum */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-23T16:55:27Z

Vsj17: /* Molecular Orbital Diagram of BH3 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|center|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|right|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-23T16:54:54Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|center|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-23T16:54:26Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|center|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

File:Vssj LUMO bh3.png

2019-05-23T16:54:03Z

Vsj17:

ICL:1905

2019-05-23T16:53:49Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_bh3.png|center|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

File:Vssj HOMO1 BH3.png

2019-05-23T16:52:30Z

Vsj17:

ICL:1905

2019-05-23T16:52:03Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).]]

[[File:vssj_LUMO_BH3.png|center|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-23T16:51:17Z

Vsj17: /* Molecular Orbital Diagram of BH3 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).

[[File:vssj_LUMO_BH3.png|center|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.

[[File:Example.jpg]]

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-23T16:50:30Z

Vsj17: /* Molecular Orbital Diagram of BH3 */

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

[[File:vssj_HOMO1_BH3.png|left|400px|thumb|This MO is an accurate portrayal of one of the HOMOs in BH3 (1e' MO - where the p orbital is vertical).

[[File:vssj_LUMO_BH3.png|center|400px|thumb|This MO is an accurate portrayal of the LUMO in BH3.

Are there any significant differences between the real and LCAO MOs?

The only significant difference observed between the real and LCAO MOs is that the MO diagram shows the atomic orbitals as they are before combination occurs, while the MOs from Gaussview have already combined them.

What does this say about the accuracy and usefulness of qualitative MO theory?

It is highly accurate and useful.

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-23T16:37:58Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

Are there any significant differences between the real and LCAO MOs?
What does this say about the accuracy and usefulness of qualitative MO theory?

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)

ICL:1905

2019-05-23T16:37:32Z

Vsj17:

== Exercise 1: Borane - BH3 ==
=== B3LYP/3-21G summary ===
[[File:bh3_321G_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a BH3 molecule using the B3LYP/3-21G basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -6.8246 -1.4177 -0.0054 0.7248 7.6960 7.8255
Low frequencies --- 1162.9713 1213.1658 1213.1685
</pre>

Frequency analysis log file: [[Media:VSSJ_BH3_freq.log| VSSJ_BH3_freq.log]]

<jmol><jmolApplet>
<title>Borane</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_BH3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised B-H bond length is 1.19231 Å.

=== Vibrational spectrum for BH3 ===

{| class="wikitable" border="1"
! Wavenumber (cm-1 !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type of vibration
|-
| 1162.97 || 93 || A2" || Yes || Out-of-plane bending.
|-
| 1213.17|| 14 || E' || Yes || Asymmetric bending (of 2 B-H bonds)
|-
| 1213.17 || 14 || E' || Yes || Asymmetric bending
|-
| 2582.36 || 0 || A1' || No || Symmetric stretching
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching (of 2 B-H bonds)
|-
| 2715.54 || 126 || E' || Yes || Asymmetric stretching
|}

=== BH3 IR Spectrum ===
[[File:bh3_infrared_spectrum.png|left|400px|thumb|The infra-red spectrum of an optimised molecule of borane.]]

Despite there obviously being 6 vibrations, only 3 are visible in borane's infra-red spectrum. This is because there are vibrations that correspond to the same wavenumber, and therefore appear as 1 intensified peak. For example, there are 2 different asymmetric bends in borane; however since they have the same wavenumber, intensity, symmetry and are both IR active, they appear as 1 peak. The same goes with the 2 different asymmetric stretches. Lastly, the vibration corresponding to v=2582.36 cm-1 is not visible on the spectrum because the symmetric stretches cancel each other out, resulting in no net dipole moment and therefore is IR inactive.

=== Molecular Orbital Diagram of BH3 ===
[[File:vssj_BH3_redrawn_MO_diagram.png|left|400px|thumb|Borane's molecular orbital diagram.]]

Are there any significant differences between the real and LCAO MOs?
What does this say about the accuracy and usefulness of qualitative MO theory?

== Exercise 2: Ammonia-Borane ==
E(NH3)= -56.55776873 au, E(BH3)= -26.61532364 au, E(NH3BH3)= -83.22468893 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22468893 - (-56.55776873 - 26.61532364) = -0.05159656 a.u. = -135.47 kJ mol-1

Looking at this obtained value for the N-B dative covalent bond strength, it is comparatively weak when also looking at N-N (167 kJ mol-1) and B-B (293 kJ mol-1). This might be because it is not a fully covalent bond, and the reason for assuming it's a weak bond is because the N-N bond is weak too (due to repulsion of the lone pairs surrounding N, leaving the single bond to be quite unstable), and yet the strength of the N-N bond is greater than the N-B bond.

== Exercise 3: Nitrogen Triiodide - NI3 ==

Frequency analysis log file: [[Media:VSSJ_NI3__FREQ.log| VSSJ_NI3_FREQ.log]]

[[File:ni3_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a NI3 molecule using the GEN basis set.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
Predicted change in Energy=-1.191918D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>Nitrogen triiodide</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_NI3_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I distance is 2.18424 Å.

== Mini project - Lewis Acids and Bases - Al2Cl4Br2 ==
=== Al2Cl4Br2 where Br atoms are trans and Cl atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL2CL4BR2_FREQ.log| VSSJ_AL2CL4BR2_FREQ.log]]

[[File:Al2Cl4Br2_freq_summary_table.png|left|400px|thumb|A summary of the data obtained from the optimisation of a Al2Cl4Br2 molecule using the GEN basis set (here Cl atoms are bridging the Al atoms).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000439 0.001800 YES
RMS Displacement 0.000151 0.001200 YES
Predicted change in Energy=-3.294505D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -5.1504 0.0023 0.0023 0.0038 1.4135 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (trans)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL2CL4BR2_FREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised Al-Br bond length is 2.27463 Å. The optimised Al-tCl bond length is 2.09378 Å. The optimised Al-μCl bond lengths are: 2.29812 Å and 2.29803 Å.

=== Al2Cl4Br2 where Br atoms are bridging Al atoms together ===
Frequency analysis log file: [[Media:VSSJ_AL_BR_BRIDGING_OPT.log| VSSJ_AL_BR_BRIDGING_OPT.log]]

<jmol><jmolApplet>
<title>Dialuminium tetrachloride dibromide (Br atoms are bridging)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>VSSJ_AL_BR_BRIDGING_OPT.log</uploadedFileContents>
</jmolApplet></jmol>

1. Determine the five possible isomers and identify the symmetry of each isomer of Al2Cl4Br2.

[[File:Al_Br_trans_Cl_bridging.png|left|400px|thumb|Isomer A. Point group = C1.]]

[[File:Al_Br_bridging.png|center|400px|thumb|Isomer B. Point group = C2.]]

[[File:Al_Br_cis.png|right|400px|thumb|Isomer C. Point group = C1.]]

[[File:Al_Br_cis2.png|left|400px|thumb|Isomer D. Point group = C2.]]

[[File:Al_Br_bridging_and_terminal.png|center|400px|thumb|Isomer E. Point group = C1.]]

2. Compute the energy of the isomers with (a) 2 bridging Br ions and (b) the isomer with trans terminal Br and bridging Cl atoms.

(a)- The energy of the isomer with bridging Br atoms is -2352.4063 a.u.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -2352.4163 a.u.

3. Determine the relative energy of these isomers in kJ/mol.

(a)- The energy of the isomer with bridging Br atoms is -6176242 kJ mol-1.
(b)- The energy of the isomer with trans terminal Br atoms and bridging Cl atoms is -6176269 kJ mol-1.

4. Discuss the relative stability of these conformers with respect to the bridging ions.

Br is a bigger atom than Cl, therefore the Al-Br bridging bond is longer than that of Al-Cl, which results in poorer orbital overlap between Al and Br. This means that the isomer where Br atoms are bridging is less stable than those where Cl atoms are bridging.

5. Determine the dissociation energy for the lowest energy conformer into 2AlCl2Br.

Dissociation energy => ΔE = E(Al2Cl4Br2) - 2E(AlCl2Br) = -2352.41629861 a.u. - (2 X -1176.79013674 a.u.) = 1.16397487 a.u. ~ 1.1640 a.u. ~ 3056 kJ mol-1

6. Is the product more or less stable than the isolated monomers?

7. Carry out a MO calculation on the lowest energy isomer (only!)