ChemWiki - User contributions [en]

Rep:Mod:c01190004

2018-05-18T07:17:04Z

Cn816: /* Vibrational spectrum for NH3-BH3 */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 120.0°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=500px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>H. research group Hunt, Patricia, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>Y.-R. Luo, Comprehensive handbook of chemical bond energies, CRC Press, 2007.</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>Y.-R. Luo, Comprehensive handbook of chemical bond energies, CRC Press, 2007.</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>
=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BBR3_OPT_PP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -1176.19014 a.u. to the optimisation run, and the gradient is low at 0.00000419 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:CNMONFREQSUM.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_MONOMER_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- 0.0023 0.0033 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted. There are no negative frequencies
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.
</pre>

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-18T07:15:30Z

Cn816: /* Molecular orbitals of BH3 */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 120.0°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=500px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>H. research group Hunt, Patricia, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>
=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BBR3_OPT_PP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -1176.19014 a.u. to the optimisation run, and the gradient is low at 0.00000419 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:CNMONFREQSUM.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_MONOMER_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- 0.0023 0.0033 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted. There are no negative frequencies
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.
</pre>

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T20:18:26Z

Cn816:

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 120.0°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=500px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_FREQ2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>
=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BBR3_OPT_PP_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -1176.19014 a.u. to the optimisation run, and the gradient is low at 0.00000419 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:CNMONFREQSUM.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_MONOMER_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- 0.0023 0.0033 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted. There are no negative frequencies
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.
</pre>

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T20:15:14Z

Cn816: /* Relative energies of the isomers */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 120.0°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=500px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -1176.19014 a.u. to the optimisation run, and the gradient is low at 0.00000419 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:CNMONFREQSUM.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_MONOMER_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- 0.0023 0.0033 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted. There are no negative frequencies
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.
</pre>

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T18:42:49Z

Cn816: /* Vibrational spectrum for BH3 */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 120.0°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=500px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -1176.19014 a.u. to the optimisation run, and the gradient is low at 0.00000419 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:CNMONFREQSUM.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_MONOMER_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- 0.0023 0.0033 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted. There are no negative frequencies
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.
</pre>

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T18:42:19Z

Cn816: /* 3_1G, B3LYP Optimisation */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 120.0°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -1176.19014 a.u. to the optimisation run, and the gradient is low at 0.00000419 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:CNMONFREQSUM.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_MONOMER_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- 0.0023 0.0033 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted. There are no negative frequencies
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.
</pre>

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:38:00Z

Cn816:

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -1176.19014 a.u. to the optimisation run, and the gradient is low at 0.00000419 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:CNMONFREQSUM.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_MONOMER_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- 0.0023 0.0033 0.0045 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted. There are no negative frequencies
<pre>
Item Value Threshold Converged?
Maximum Force 0.000081 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000974 0.001200 YES
Predicted change in Energy=-1.810813D-07
Optimization completed.
-- Stationary point found.
</pre>

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

File:CN MONOMER OPT FREQ.LOG

2018-05-17T14:36:58Z

Cn816:

File:CNMONFREQSUM.PNG

2018-05-17T14:34:59Z

Cn816:

Rep:Mod:c01190004

2018-05-17T14:27:59Z

Cn816: /* Isomer with trans terminal Br and bridging Cl */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:25:25Z

Cn816:

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>
==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Molecular orbitals of lowest energy conformer (trans Br, bridging Cl) ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:24:36Z

Cn816: /* Frequency Analysis */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000044 0.001200 YES
Predicted change in Energy=-2.950687D-09
Optimization completed.
-- Stationary point found.
</pre>

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>
==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:23:32Z

Cn816: /* Frequency analysis */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, there are now negative frequencies and hence this frequency analysis is accepted.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000779 0.001800 YES
RMS Displacement 0.000426 0.001200 YES
Predicted change in Energy=-2.165787D-07
Optimization completed.
-- Stationary point found.
</pre>
==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>
==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:21:45Z

Cn816: /* Frequency analysis */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-8.435065D-11
Optimization completed.
-- Stationary point found.
</pre>

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>
==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:20:04Z

Cn816: /* Frequency analysis */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000081 0.000300 YES
Maximum Displacement 0.000635 0.001800 YES
RMS Displacement 0.000318 0.001200 YES
Predicted change in Energy=-1.536878D-07
Optimization completed.
-- Stationary point found.
</pre>

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>
==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:17:32Z

Cn816:

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>
==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

A frequency calculation was run using GEN, B3LYP method.
<gallery widths=250px heights=300px >
File:CNBRIDGE.PNG|Summary of results for frequency analysis of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Low frequencies --- -5.1749 -5.0366 -3.1484 -0.0034 -0.0016 -0.0015
Low frequencies --- 14.8259 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000279 0.001800 YES
RMS Displacement 0.000136 0.001200 YES
Predicted change in Energy=-4.311968D-10
Optimization completed.
-- Stationary point found.
</pre>
Link to log fileː [[:File:CN_BRIDGEBR_OPT_FREQ.LOG]]

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

File:CN BRIDGEBR OPT FREQ.LOG

2018-05-17T14:16:23Z

Cn816:

File:CNBRIDGE.PNG

2018-05-17T14:13:18Z

Cn816:

Rep:Mod:c01190004

2018-05-17T14:10:26Z

Cn816: /* jmols of optimised isomers */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:09:39Z

Cn816: /* Isomer with two bridging Br */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

File:CN TRANSBR OPT FREQ.LOG

2018-05-17T14:09:20Z

Cn816: Cn816 uploaded a new version of File:CN TRANSBR OPT FREQ.LOG

Rep:Mod:c01190004

2018-05-17T14:02:21Z

Cn816: /* Frequency analysis */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.
<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>

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T14:01:31Z

Cn816: /* Frequency Analysis */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T13:57:45Z

Cn816: /* jmol of isomer with bridging Br */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T13:55:00Z

Cn816:

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999°
<gallery widths=350px heights=400px>
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== jmols of optimised isomers ===
==== jmol of isomer with trans Br, bridging Cl ====
<jmol><jmolApplet>
<title> Isomer with trans Br, bridging Cl </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_TRANSBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== jmol of isomer with bridging Br ====
<jmol><jmolApplet>
<title> Isomer with bridging Br </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BRIDGEBR_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

File:CN BRIDGEBR OPT.LOG

2018-05-17T13:54:50Z

Cn816: Cn816 uploaded a new version of File:CN BRIDGEBR OPT.LOG

Rep:Mod:c01190004

2018-05-17T13:46:04Z

Cn816:

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
<jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
<jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
<jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
<jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T13:41:43Z

Cn816:

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== References ==

Rep:Mod:c01190004

2018-05-17T13:40:30Z

Cn816: /* Project section: Lewis acids and bases. */

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and basesː Al2Cl4Br2 ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== Structure ==

Rep:Mod:c01190004

2018-05-17T13:39:27Z

Cn816:

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

=== Molecular orbitals of lowest energy conformer ===
Three occupied MOs were chosen and analysed as below.
<gallery widths=800px heights=600px >
File:CN152.PNG|Highly antibonding orbital
File:CN39.PNG|Highly bonding orbital
File:Cn42.PNG|Bonding orbital

</gallery>

== Structure ==

File:Cn42.PNG

2018-05-17T13:36:34Z

Cn816:

File:CN39.PNG

2018-05-17T13:35:49Z

Cn816:

File:CN152.PNG

2018-05-17T13:35:09Z

Cn816:

Rep:Mod:c01190004

2018-05-17T13:27:23Z

Cn816: /* Dissociation energy of lowest energy conformer */

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, C2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>

=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Molecular orbitals of lowest energy conformer ====

== Structure ==

Rep:Mod:c01190004

2018-05-17T11:43:11Z

Cn816: /* Different isomers and their symmetries */

Rep:Mod:c01190004

2018-05-17T11:13:11Z

Cn816: /* Lowest energy conformerː Bridging Cl */

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, D2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|Results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Molecular orbitals of lowest energy conformer ====

== Structure ==

Rep:Mod:c01190004

2018-05-17T11:11:19Z

Cn816: /* Lowest energy conformerː Bridging Cl */

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, D2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Molecular orbitals of lowest energy conformer ====

== Structure ==

Rep:Mod:c01190004

2018-05-17T11:05:23Z

Cn816: /* 6_31G (d,p), B3LYP Optimisation */

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>

=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, D2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Structure ==

Rep:Mod:c01190004

2018-05-16T15:52:50Z

Cn816:

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
As seen from the Summary below, the total energy is the same at -64.43645 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Cn_bbr3freq.PNG|BBr3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_BBR3_OPT_PP_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.6583 -3.3109 -2.2850 -0.0002 0.0001 0.0002
Low frequencies --- 155.8429 155.9360 267.6978
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, D2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Structure ==

File:CN BBR3 OPT PP FREQ.LOG

2018-05-16T15:52:13Z

Cn816:

File:Cn bbr3freq.PNG

2018-05-16T15:49:37Z

Cn816:

Rep:Mod:c01190004

2018-05-16T15:44:25Z

Cn816: /* Optimisation using pseudo potentials */

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_Bbr3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
A frequency run was done on the

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, D2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Structure ==

File:CN Bbr3 OPT PP.LOG

2018-05-16T15:43:08Z

Cn816:

Rep:Mod:c01190004

2018-05-16T15:40:21Z

Cn816: /* Optimisation using pseudo potentials */

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3</suɓ> using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_BH3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
A frequency run was done on the

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, D2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Structure ==

Rep:Mod:c01190004

2018-05-16T15:06:29Z

Cn816:

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3-NH3 using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_BH3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
A frequency run was done on the

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, D2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP method.

As seen from the Summary below, the total energy is the same at -2352.41630 a.u. to the optimisation run, and the gradient is low at 0.00000410 a.u. (<0.001 a.u.)

<gallery widths=350px heights=400px >
File:Cn_trans_freqsum.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_TRANSBR_OPT_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -5.1504 -0.0036 -0.0021 -0.0011 1.4134 2.0504
Low frequencies --- 18.1470 49.1065 73.0086
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

== Structure ==

File:CN TRANSBR OPT FREQ.LOG

2018-05-16T15:05:50Z

Cn816:

File:Cn trans freqsum.PNG

2018-05-16T15:05:14Z

Cn816:

Rep:Mod:c01190004

2018-05-16T14:58:18Z

Cn816:

== EX3 Section ==
We expect to see:
* a title identifying the molecule
* the method and basis set defined
* an image of the summary table produced by gaussview (after optimisation)
* the "Item" table (in pre tags) from the *.log file (from the optimisation job)
* a link to the frequency and/or population analysis files
* low frequencies data (in pre tags) from the *.log file (from the frequency job)
* a rotatable 3d jmol file/image of the optimised structure

== BH3 ==

=== 3_1G, B3LYP Optimisation ===
Optimised bond length= 1.19467 a.u.

Optimised bond angle = 119.999 °
<gallery widths=350px heights=400px >
File:Bh3_results_summary.PNG|BH3 optimisation summary of results

</gallery>

Optimisation is complete as the gradient norm has reached a low value of 0.00008756 a.u. ( <0.001 a.u. )

Link to log file: [[:File:CN_BH3_OPT.LOG]]

Extract of Item table from the .log file:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000692 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635268D-07
Optimization completed.
-- Stationary point found.
</pre>
The important information is in the part below "Item" this tells us that the forces are converged (remember force is the gradient or slope of the energy vs distance graph. It also tells us that the placements are converged, this means that for a small displacement the energy does not change

''Q: What definition would you choose for the existence of a bond?''

The definition i would choose would be that the bond distance is lesser than half of the sum of the Van Der Waal's radii of the two atoms in consideration.

=== 6_31G (d,p), B3LYP Optimisation ===
The output of the 3_31G run was utilised to run a 2nd optimisation using a higher level basis set: 6_31G (d,p)

Running the 6_31g calculation provides a molecule with the the optimised structure as can be intepreted from the low gradient of 0.00008206 a.u. ( <0.001 a.u.)and convergence has occurred as from the Item table in the .log file.

<gallery widths=350px heights=400px >
File:631g_bh3_results_summary.PNG|BH3 optimisation (using higher level basis set: 6-31G(d,p))
</gallery>

Link to log fileː [[:File:CN_BH3_631G_OPT.LOG]]

Extract of Item table from log fileː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000204 0.000450 YES
RMS Force 0.000099 0.000300 YES
Maximum Displacement 0.000875 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.452109D-07
Optimization completed.
-- Stationary point found.
</pre>
We can hence conclude that the run has concluded properly.

Total energy (631g): -26.61532 a.u.

Total energy (31g)= -26.46226 a.u.

Energy difference = 0.15305 a.u.

The optimisation was re-run with a D3H symmetry imposed on it.

Following the optimisation run, a D3H symmetry molecule was obtained.

<gallery widths=350px heights=400px >
File:D3h631g_bh3_results_summary.PNG|BH3 optimisation using 6-31G(d,p), constraining to D3H
</gallery>
Link to log file: [[:File:CN_BH3_SYM_OPT1.LOG]]

Extract of the Item table ː
<pre>
Item Value Threshold Converged?
Maximum Force 0.000161 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000639 0.001800 YES
RMS Displacement 0.000418 0.001200 YES
Predicted change in Energy=-1.545207D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of BH3 ===
jmol><jmolApplet>
<title> BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_SYM_OPT1.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
A frequency run was done on the output of the BH3 6_31G optimisation run, and the energy is the same as the input at -26.61532 a.u. as seen below.

<gallery widths=350px heights=400px >
File:BH3O.PNG|BH3 frequency run using optimisation with 6-31G(d,p) basis set
</gallery>

Link to log fileː [[:File:CN_BH3_SYM_FREQ2.LOG]]
<pre>
Low frequencies --- -0.2433 -0.1118 -0.0055 44.4606 45.6068 45.6075
Low frequencies --- 1163.6172 1213.6006 1213.6033
</pre>The lowest frequency range is within ±50 cm-1 range, and hence this run is accepted as successful.

The formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for BH3 ====
{| class="wikitable"
!Vibrations (cm-1 )
!Intensities(arbitrary)
!Symmetry
!IR active
!Type
|-
|1163
|6.6
|A2"
|Yes
|Symmetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|1213
|1
|E'
|Very slightly
|Asymetric bend
|-
|2580
|0
|A1'
|No
|Symmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|-
|2713
|9
|E'
|Yes
|Asymmetric stretch
|}

Snapshot of the IR spectrum:
<gallery widths=350px heights=400px >
File:IR_SPECTRUM_BH3.PNG|IR spectrum of BH3
</gallery>There are only 3 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so are the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The fourth vibration is not observed as it has an intensity of 0 and will not be experimentally observable. Hence only three peaks corresponding to the 1st, 2nd, 3rd, 5th, 6th vibrations in the table (of which 2nd, 3rd are degenerate and 5th,6th are degenerate), will be observed.

=== Molecular orbitals of BH3 ===

[[File:MOdiagram.PNG]]

Modified MO diagram of BH3 with the calculated MOs, adapted from <ref><nowiki>http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/7a_molecular_orbitals.html</nowiki></ref>.

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

There are no significant differences between the real and LCAO MOs as can be observed in the MO diagram above.

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

This says that qualitative MO theory is actually rather accurate and useful in predicting the real life molecular orbitals.

== NH3 ==

=== Optimisation using 6_31G (d,p) , B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successful completed as can be seen from the low gradient below 0.001 a.u. and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:Nh3_results_summary.PNG|NH3 results summary for optimisation with 6-31G(d,p) basis set
</gallery>

Link to log file: [[:File:CN_NH3_631G_OPT.LOG]]

Extract of Item table from .log file ː

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000010 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-7.830786D-11
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3 ===
jmol><jmolApplet>
<title> NH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3_631G_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -56.55777 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3_freq_results_summary.PNG|NH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -11.6527 -11.6490 -0.0048 0.0332 0.1312 25.5724
Low frequencies --- 1089.6616 1694.1736 1694.1736
</pre>The lowest frequency range is within the ±50 cm-1 range, the formally zero frequencies are well separated from the lowest energy positive frequency at 1089 cm-1 and the large formally zero frequencies are due to the low level of the basis set and relatively relaxed convergence and integration criteria, which can occur for small molecules like NH3.

==== Vibrational spectrum for NH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|1089
|538
|A
|Yes
|Symmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|1694
|50
|E
|Yes
|Asymmetric bend
|-
|3461
|4
|A
|No
|Symmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|-
|3589
|1
|E
|No
|Asymmetric stretch
|}
Snapshot of the spectrum:
<gallery widths=400px heights=250px >
File:IR_SPECTRUM_NH3.PNG|NH3 IR spectrum
</gallery>There are less than 6 peaks in the spectrum. This is because the 2nd, 3rd vibrations are degenerate, and so ar the 4th and 5th vibrations in the table, for within these pairs, the vibrations have the same wavenumber and intensity given that wavenumber is proportional to energy. Because they are degenerate and of the same energy, they give rise to a single peak in the spectra. The last two three vibrations (of which two are degenerate) have very low relative intensities and these vibrations will not be experimentally observable. Hence only two peaks corresponding to the first three vibrations in the table (of which two are degenerate), will be observed.

== NH3-BH3 ==

=== Optimisation using 6_31G, B3LYP ===
A 6_31G optimisation with B3LYP method was also run for the NH3 molecule. The run has successfully completed as can be seen from the low gradient below 0.0001 and convergence as seen from the Item table below.

<gallery widths=350px heights=400px >
File:NH3BH3_SUMMARY.PNG|NH3-BH3 results summary
</gallery>
Link to the log file: [[:File:CN_NH3BH3_OPT.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000771 0.001800 YES
RMS Displacement 0.000338 0.001200 YES
Predicted change in Energy=-2.028054D-07
Optimization completed.
-- Stationary point found.
</pre>
=== jmol of NH3-BH3 ===
jmol><jmolApplet>
<title> NH3-BH3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency analysis ===
As seen from the Summary below, the total energy is the same at -83.22469 a.u. to the optimisation run.

<gallery widths=350px heights=400px >
File:Nh3nh3_frew.PNG|NH3-BH3 results summary for the frequency run
</gallery>
Link to the log file: [[:File:CN_NH3BH3_FREQ.LOG]]

Extract of the "low frequencies" from the .log file
<pre>
Low frequencies --- -0.0613 -0.0448 -0.0067 22.1060 22.1116 40.5984
Low frequencies --- 265.9056 632.3740 640.1221
</pre>
The lowest frequency range is within the ±50 cm-1 range, and hence this frequency analysis is accepted.

==== Vibrational spectrum for NH3-BH3 ====
{| class="wikitable"
!Wavenumber(cm-1)
!Intensity (Arbitrary units)
!Symmetry
!IR active?
!type
|-
|265
|0
|A2
|No
|
|-
|632
|5.6
|A1
|Slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|640
|1.4
|E
|Very slightly
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1069
|16.2
|E
|Yes
|
|-
|1196
|43.6
|A1
|Yes
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1203
|1.4
|E
|Very slightly
|
|-
|1330
|45.4
|A1
|Yes
|
|-
|1676
|11
|E
|Slightly
|
|-
|1676
|11
|E
|Slightly
|
|-
|2470
|26.9
|A1
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|2530
|92.5
|E
|Yes
|
|-
|3462
|1
|A1
|very very slightly
|
|-
|3579
|11.2
|E
|Slightly
|
|-
|3579
|11.2
|E
|Slightly
|}
Q: Look at ''your number, is it a sensible value? How do you know what a sensible value is? (Hint: this is a bond energy, so what "ballpark" value should it have?''

This is a sensible value, as it comes close to the single bond dessociation energies that are usually within the range of 150–400 kJ/mol<ref><nowiki>https://opentextbc.ca/chemistry/chapter/7-5-strengths-of-ionic-and-covalent-bonds/</nowiki></ref>

Also it is a negative value as it should be, as no bonds are being broken but a bond between B and N is being formed, which will then be exothermic.

''Q: Based on your energy calculation is the B-N dative bond weak, medium or strong? What comparison have you made to come to this conclusion?''

Based on the energy calculations, the B-N dative bond is weak, as it is lower in magnitude than the B-N bond dissociation energy<ref><nowiki>http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf</nowiki></ref> at 377.9 kJmol-1, which is taken from a molecule in which there is a B-N single covalent bond.

== BBr3 ==

=== Optimisation using pseudo potentials ===

<gallery widths=250px heights=300px >
File:Bbr3genopt.PNG|Summary of results for optimisation of BBr3-NH3 using pseudo-potentials.
</gallery>

Link to log fileː [[:File:CN_BH3_OPT_PP.LOG]]

Item table shows convergence and a successful run.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000154 0.001800 YES
RMS Displacement 0.000080 0.001200 YES
Predicted change in Energy=-3.282217D-09
Optimization completed.
-- Stationary point found.
</pre>

=== jmol for BBr3 ===
jmol><jmolApplet>
<title> BBr3 molecule </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CN_BH3_OPT_PP.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Frequency Analysis ===
A frequency run was done on the

== Project section: Lewis acids and bases. ==
=== Different isomers and their symmetries ===

<gallery widths=300px heights=200px>
File:Cn_p1.PNG|Cl bridging, cis, Cs point group
File:Cn_p2.PNG|Cl bridging, trans, D2H point group
File:Cn_p5.PNG|CL bridging, both Br on same Al atom, C2V point group
File:Cn_p4.PNG|CL,Br bridge, C1 point group
File:Cn_p3.PNG|Br bridging, D2H point group

</gallery>
=== Energies ===

==== Isomer with trans terminal Br and bridging Cl ions ====
An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000413 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:Cn transright.PNG|Summary of results for optimisation of trans isomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-6.046439D-10
Optimization completed.
-- Stationary point found.

</pre>
Link to log fileː [[:File:CN_TRANSBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.41630 a.u.

==== Isomer with two bridging Br ions ====

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00000182 (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_BRIDGEBR_1.PNG|Summary of results for optimisation of isomer with bridging Br using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000038 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-2.660957D-10
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_BRIDGEBR_OPT.LOG]]

Energy of the isomer was calculated to be -2352.40631 a.u.

==== Relative energies of the isomers ====
Energy (isomer with trans Br ions, bridging Cl) -2352.41630 a.u. = -6176269.4661 kJmol-1

Energy(isomer with bridging Br)= -2352.40631 a.u. = -6176243.2374 kJmol-1

|Energy difference|ː 26.22871 kJmol-1

The lower energy isomer is that of the one with bridging CL- ions. This might be because Cl is more electronegative than Br, and hence is better able to stabilise the negative charge as a bridging ligand, than the Br. Additionally, Br is much larger in size (185 pm) compared to Cl (175 pm) given that it has an extra shell of electrons.Hence it would prefer to be at the terminal positions where there is less steric hindrance, having a Br-Al-Br angle of 120 degrees rather than constrained between the two Al atoms where the bond angle is approximately 60 degrees (as in a triangle formation).

The energy difference between the two conformers is very subtle as Br is large and has diffuse orbitals that can still interact with the Al orbitals, and coordinate to them.

==== Dissociation energy of lowest energy conformer ====

To determine the lowest energy conformer, an optimisation was carried out on the AlCl2Br momomer using the same basis set (GEN, B3LYP).

An optimisation using GEN pseudopotentials, B3LYP method was carried out on the built structure.
As can be seen from the low gradient of 0.00004196 a.u. (<0.001 a.u.) of the run from the summary table below and the convergence as can be seen from the Item table extracted from the .log file, optimisation was complete.

<gallery widths=250px heights=300px >
File:CN_MONO1.PNG|Summary of results for optimisation of monomer using pseudo-potentials.
</gallery>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000205 0.000450 YES
RMS Force 0.000096 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000778 0.001200 YES
Predicted change in Energy=-1.597568D-07
Optimization completed.
-- Stationary point found.
</pre>

Link to log fileː [[:File:CN_MONOMER_OPT.LOG]]

Energy of the monomer was calculated to be -1176.19014 a.u. = -3088087.44781 kJmol-1

Dissociation energy = [ 2(-3088087.44781) -(-6176269.4661) ] kJmol-1
= 94.57048 kJmol-1

The product is more stable than the isolated monomers, given that the energy of the isomer is lower than the sum of two monomers by 94.57048 kJmol-1. This is for the bridging bonds relieve the electron deficiency on the Al atoms and lower the energy of the entire system. Energy must be supplied into the system to break these stabilising bridging bonds and produce the higher energy less stable monomers.

=== Lowest energy conformerː Bridging Cl ===
==== Frequency analysis ====
A frequency calculation was run using GEN, B3LYP AN

== Structure ==

File:CN MONOMER OPT.LOG

2018-05-16T14:57:39Z

Cn816: Cn816 uploaded a new version of File:CN MONOMER OPT.LOG

File:CN MONO1.PNG

2018-05-16T14:55:03Z

Cn816: