2018-05-25T12:02:26Z

Hyc116: /* NH3BH3 */

==BH3==

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_bh3_631g_opt_summarytable.png]]

The above summary table was obtained after the 2nd optimisation of BH3 (after the initial optimisation using the 3-21G basis set). Notice how the symmetry is incorrect and shown as Cs. This is because the symmetry was manually broken at the beginning by changing the bond length of B-H bonds. The point group was manually adjusted and the molecule was optimised again before the frequency analysis and the new summary table is attached below.

[[file:Hyc116_bh3_correctsummarytable.png]]

The above summary table was obtained from the optimisation after adjusting the symmetry. The point shown in this summary table is D3h, which is the correct for BH3.

'''Items table'''

Below is the items table taken from the optimisation with the correct point group.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116 BH3 FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

'''jmol of BH3'''
<jmol><jmolApplet>
<title>optimised BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum===

{| class="wikitable"
!wavenumber (cm-1)
!Intensity (arbitrary units)
!symmetry
!IR active?
!type
|-
|1163
|93
|A2' '
|Yes
|Out of plane bend
|-
|1213
|14
|E'
|Very slight
|Bend
|-
|1213
|14
|E'
|Very slight
|Bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

'''IR spectrum'''

[[file:Hyc116_ir_bh3.png|400*600]]

There are only three peaks on the IR spectrum of BH3, despite that there are 6 vibrational modes for the molecule. As shown in the table above, the symmetric stretching mode with A1 symmetry at 2582 cm-1 is not IR active; naturally, that vibrational mode doesn’t give a peak on the IR spectrum. As shown from the table, two pairs of vibrational modes, the bond angle deformation/bend at 1213 cm-1 and the asymmetric bond stretch at 2716 cm-1, are degenerate with the symmetry label E. This means that they have the same energy, and hence give the same wavenumber on the IR spectrum. Each pair of degenerate vibrational modes give rise to one peak. This leaves three peaks, as confirmed by the IR spectrum above.

===Molecular orbitals of BH3===

[[file:hyc116_bh3_MO_diagram.png]]

The above molecular orbital diagram was taken from Dr Patricia Hunt's Lecture 4 Tutorial Problem Model Answers.<ref>P. Hunt, "Lecture 4 Tutorial Problem Model Answers", 2 (2018)</ref> Diagrams of the "real" MOs were obtained from Gaussian.

There is no significant difference between the LCAO MOs and the real ones. Features such as orbital phases are shown clearly on both the LCAO MOs and the real MOs, illustrating the bonding/anti-bonding characters of the molecular orbitals. This suggests that the the qualitative MO theory is highly accurate and useful when studying the molecular orbitals of molecules.

==Associated energies: ammonium borane==

===NH3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_nh3_631g_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_NH3_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''jmol of NH3'''
<jmol><jmolApplet>
<title>optimised NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_nh3bh3_631g_summarytable1.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000121 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000501 0.001800 YES
RMS Displacement 0.000293 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_NH3BH3_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -0.0014 -0.0011 -0.0006 6.9624 20.4518 43.5542
Low frequencies --- 266.4530 632.2458 639.0504
</pre>

'''jmol of NH3BH3'''
<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association energy===

E(BH3) (using the optimisation with the correct symmetry) = -26.61532363 a.u. = -26.61532 a.u. (5 d.p.)

E(NH3) = -56.55776873 a.u. = -56.55777 a.u. (5 d.p.)

E(NH3BH3) = -83.22468893 a.u. = -83.22469 a.u. (5 d.p.)

Carrying out calculations using numbers which has already been rounded up can possibly result in errors in the last digit. Hence, here the calculations were carried out using the numbers provided from the optimisations (i.e. with more decimal places than necessary); the answer was then rounded up to the desired accuracy.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE = -83.22468893 - (-56.55776873 + -26.61532363) = -0.05159657 a.u.

ΔE = -0.05160 a.u. (5 d.p.)

'''Converting energy from a.u. to kJ/mol'''
An atomic unit for energy is Hartree, which is equal to 2625.5 kJ/mol.
<ref>https://cccbdb.nist.gov/hartree.asp (Accessed: 22.05.2018)</ref>

So ΔE in kJ/mol = -0.05159657 * 2625.5 = -135.466794535 kJ/mol

ΔE = -135 kJ/mol (nearest integer)

The energy difference calculated above comes from the formation of the B-N dative bond. It is a relatively weak bond. According to a bond energy data sheet provided by the University of California,<ref>https://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf (Accessed: 24.05.2018)</ref> the bond energy of the C-C bond of an ethane molecule is 368 kJ/mol. This is a fair comparison to the NH3BH3 molecule as the two molecules have the same structure, only with the carbon atoms on ethane swapped for Boron and Nitrogen in NH3BH3

==Using a mixture of basis-sets and pseudo-potentials==

===BBr3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: Boron: 6-31G(d,p) ; Br: LANL2DZ

Larger calculations are often sent to a web-server to run on a high-performance computer instead of a desktop. In order to experience and learn to use a web-server, the optimisation and the frequency analysis for BBr3</sub were both sent and done on a server instead of the desktop. The calculation results were downloaded from the web-server once they were finished.

'''Summary table'''

[[file:Hyc116_bbr3_opt_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:Hyc116_bbr3_freq.log]]

Attached above is the frequency file saved onto the computer from the SCAN server portal. The frequency file was also published on the chemistry database DSpace. {{DOI|10042/202442}}

'''Frequencies'''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''jmol of BBr3'''
<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Hyc116_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_c6h6_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_C6H6_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0089 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

'''jmol of C6H6'''
<jmol><jmolApplet>
<title>optimised Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_C6H6_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_borazine_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_BORAZINE_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -12.6626 -12.6626 -8.9272 -0.0211 -0.0104 -0.0104
Low frequencies --- 289.1112 289.1112 403.8613
</pre>

'''jmol of Borazine'''
<jmol><jmolApplet>
<title>optimised Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Charge distribution===

An NBO charge analysis was carried out on both the optimised benzene and borazine. Visualisations of the charge distribution are shown in the table below, with the colour range going from -1.102 to 1.102 for both molecule. This large scale was chosen as it allows direct comparison of the charge on any atoms in these two molecules and shows the relative magnitude of charges on all these atoms. Negative charges are shown in red, and positive charges are shown in green. A neutral charge is displayed in black, so the smaller a charge is (positive or negative), the darker its colour representation is. Larger charges are shown in brighter colours. The charges are also displayed on the atoms as numbers with a neutral charge being zero. Negative charges are shown as negative number and positive charges are shown as positive numbers.

{| class="wikitable"
!
!Benzene
!Borazine
|-
!Visualisation of charge distribution
|[[File:Hyc116_benzene_charge_distribution1.png|500x500px|thumb|centre|Charge distribution of Benzene visualisation]]
|[[File:Hyc116_borazine_charge_distribution1.png|500x500px|thumb|centre|Charge distribution of Borazine visualisation]]
|-
!Charge
|Carbon: -0.239

Hydrogen: 0.239
|Nitrogen: -1.102

Boron: 0.747

Hydrogen (bonded to N): 0.432

Hydrogen (bonded to B): -0.077
|-
!Discussion
|From the visualisation, it is shown that there is a slightly negative charge on the carbon atoms, and a positive charge of the same magnitude on the hydrogen atoms. All the carbon atoms have the same charge as they are in identical environments. The same applies to all the hydrogen atoms. This is due to the highly symmetrical structure of benzene. Since the same colour scale was used for both benzene and borazine, and the charges are much smaller in magnitude on atoms in benzene than atoms on borazine, the colours on the charge distribution visualisation is much darker.
|From the colours displayed on the charge distribution visualisation as well as the charge values, it is shown that nitrogen has a relatively large negative charge, while boron has a positive charge. This is due to the difference in electrogenativity between these atoms: nitrogen atoms are more electronegative than boron and tends to attract electrons towards themselves. It is worth noting that the hydrogen atoms do not all have the same charge. The hydrogen atoms bonded to boron have a slightly negative charge, and the ones bonded to nitrogen have a small positive charge.

The fact that the same colour scale was used for both molecules comes in helpful here. It allows the charges on atoms to be compared directly. For example, just from looking at the colours, one can tell that or example, even though both carbon and nitrogen are electronegative, nitrogen is much more electronegative, which is quantitatively shown by Pauling's electronegativity scale.<ref>http://www.tutor-homework.com/Chemistry_Help/electronegativity_table/electronegativity.html (Accessed: 24.0502018</ref>
|}

===Comparative MOs of Benzene and Borazine===

{| class="wikitable"
!
!Benzene
!Borazine
!Comparison and Discussion
|-
!1st comparative pair
|[[File:Hyc116_benzene_1st_MO_pair_7.png|200x200px|centre]]
|[[File:Hyc116_borazine_1st_MO_pair_level9.png|200x200px|centre]]
|MO 9 of both benzene and borazine are comparable. They both show delocalised molecular orbital with an overall bonding character. There is a nodal plane across the molecular orbitals for both benzene and borazine. For benzene, there is contribution from all the carbon and hydrogen s orbitals. Moreover, the molecular orbitals are symmetric to their counterpart of opposite phase. That is not the case for borazine; they are less symmetric in borazine. Nitrogen atoms are more electronegative than boron atoms and pull electron density towards themselves, resulting in a larger MO. There is contribution from all the boron and nitrogen s orbitals, and three of the hydrogen s orbitals, though not all of them.
|-
!2nd comparative pair
|[[File:Hyc116_benzene_2nd_MO_pair_10.png|200x200px|centre]]
|[[File:Hyc116_borazine_2nd_MO_pair_level11.png|200x200px|centre]]
|
|-
!3rd comparative pair
|[[File:Hyc116_benzene_3rd_MO_pair_21.png|200x200px|centre]]
|[[File:Hyc116_borazine_3rd_MO_pair_level21.png|200x200px|centre]]
|
|}

===Aromaticity: some theories===

==References==
{{reflist}}

File:Hyc116 nh3bh3 631g summarytable1.png

2018-05-25T12:01:38Z

Hyc116:

2018-05-24T16:10:50Z

Hyc116: /* Comparative MOs of Benzene and Borazine */

==BH3==

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_bh3_631g_opt_summarytable.png]]

The above summary table was obtained after the 2nd optimisation of BH3 (after the initial optimisation using the 3-21G basis set). Notice how the symmetry is incorrect and shown as Cs. This is because the symmetry was manually broken at the beginning by changing the bond length of B-H bonds. The point group was manually adjusted and the molecule was optimised again before the frequency analysis and the new summary table is attached below.

[[file:Hyc116_bh3_correctsummarytable.png]]

The above summary table was obtained from the optimisation after adjusting the symmetry. The point shown in this summary table is D3h, which is the correct for BH3.

'''Items table'''

Below is the items table taken from the optimisation with the correct point group.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116 BH3 FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

'''jmol of BH3'''
<jmol><jmolApplet>
<title>optimised BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum===

{| class="wikitable"
!wavenumber (cm-1)
!Intensity (arbitrary units)
!symmetry
!IR active?
!type
|-
|1163
|93
|A2' '
|Yes
|Out of plane bend
|-
|1213
|14
|E'
|Very slight
|Bend
|-
|1213
|14
|E'
|Very slight
|Bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

'''IR spectrum'''

[[file:Hyc116_ir_bh3.png|400*600]]

There are only three peaks on the IR spectrum of BH3, despite that there are 6 vibrational modes for the molecule. As shown in the table above, the symmetric stretching mode with A1 symmetry at 2582 cm-1 is not IR active; naturally, that vibrational mode doesn’t give a peak on the IR spectrum. As shown from the table, two pairs of vibrational modes, the bond angle deformation/bend at 1213 cm-1 and the asymmetric bond stretch at 2716 cm-1, are degenerate with the symmetry label E. This means that they have the same energy, and hence give the same wavenumber on the IR spectrum. Each pair of degenerate vibrational modes give rise to one peak. This leaves three peaks, as confirmed by the IR spectrum above.

===Molecular orbitals of BH3===

[[file:hyc116_bh3_MO_diagram.png]]

The above molecular orbital diagram was taken from Dr Patricia Hunt's Lecture 4 Tutorial Problem Model Answers. <ref>P. Hunt, "Lecture 4 Tutorial Problem Model Answers", 2 (2018)</ref>. Diagrams of the "real" MOs were obtained from Gaussian.

There is no significant difference between the LCAO MOs and the real ones. Features such as orbital phases are shown clearly on both the LCAO MOs and the real MOs, illustrating the bonding/anti-bonding characters of the molecular orbitals. This suggests that the the qualitative MO theory is highly accurate and useful when studying the molecular orbitals of molecules.

==Associated energies: ammonium borane==

===NH3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_nh3_631g_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_NH3_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''jmol of NH3'''
<jmol><jmolApplet>
<title>optimised NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_nh3bh3_631g_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000515 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_NH3BH3_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -0.0014 -0.0011 -0.0006 6.9624 20.4518 43.5542
Low frequencies --- 266.4530 632.2458 639.0504
</pre>

'''jmol of NH3BH3'''
<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association energy===

E(BH3) (using the optimisation with the correct symmetry) = -26.61532363 a.u. = -26.61532 a.u. (5 d.p.)

E(NH3) = -56.55776873 a.u. = -56.55777 a.u. (5 d.p.)

E(NH3BH3) = -83.22468893 a.u. = -83.22469 a.u. (5 d.p.)

Carrying out calculations using numbers which has already been rounded up can possibly result in errors in the last digit. Hence, here the calculations were carried out using the numbers provided from the optimisations (i.e. with more decimal places than necessary); the answer was then rounded up to the desired accuracy.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE = -83.22468893 - (-56.55776873 + -26.61532363) = -0.05159657 a.u.

ΔE = -0.05160 a.u. (5 d.p.)

'''Converting energy from a.u. to kJ/mol'''
An atomic unit for energy is Hartree, which is equal to 2625.5 kJ/mol. <ref>https://cccbdb.nist.gov/hartree.asp (Accessed: 22.05.2018)</ref>

So ΔE in kJ/mol = -0.05159657 * 2625.5 = -135.466794535 kJ/mol

ΔE = -135 kJ/mol (nearest integer)

The energy difference calculated above comes from the formation of the B-N dative bond. It is a relatively weak bond. According to a bond energy data sheet provided by the University of California, <ref>https://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf (Accessed on 24.05.2018)</ref> the bond energy of the C-C bond of an ethane molecule is 368 kJ/mol. This is a fair comparison to the NH3BH3 molecule as the two molecules have the same structure, only with the carbon atoms on ethane swapped for Boron and Nitrogen in NH3BH3

==Using a mixture of basis-sets and pseudo-potentials==

===BBr3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: Boron: 6-31G(d,p) ; Br: LANL2DZ

'''Summary table'''

[[file:Hyc116_bbr3_opt_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:Hyc116_bbr3_freq.log]]

Attached above is the frequency file saved onto the computer from the SCAN server portal. The frequency file was also published on the chemistry database DSpace. {{DOI|10042/202442}}

'''Frequencies'''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''jmol of BBr3'''
<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Hyc116_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_c6h6_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_C6H6_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0089 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

'''jmol of C6H6'''
<jmol><jmolApplet>
<title>optimised Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_C6H6_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_borazine_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_BORAZINE_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -12.6626 -12.6626 -8.9272 -0.0211 -0.0104 -0.0104
Low frequencies --- 289.1112 289.1112 403.8613
</pre>

'''jmol of Borazine'''
<jmol><jmolApplet>
<title>optimised Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Charge distribution===

An NBO charge analysis was carried out on both the optimised benzene and borazine. Visualisations of the charge distribution are shown in the table below, with the colour range going from -1.102 to 1.102 for both molecule. This large scale was chosen as it allows direct comparison of the charge on any atoms in these two molecules and shows the relative magnitude of charges on all these atoms. Negative charges are shown in red, and positive charges are shown in green. A neutral charge is displayed in black, so the smaller a charge is (positive or negative), the darker its colour representation is. Larger charges are shown in brighter colours. The charges are also displayed on the atoms as numbers with a neutral charge being zero. Negative charges are shown as negative number and positive charges are shown as positive numbers.

{| class="wikitable"
!
!Benzene
!Borazine
|-
!Visualisation of charge distribution
|[[File:Hyc116_benzene_charge_distribution1.png|500x500px|thumb|centre|Charge distribution of Benzene visualisation]]
|[[File:Hyc116_borazine_charge_distribution1.png|500x500px|thumb|centre|Charge distribution of Borazine visualisation]]
|-
!Charge
|Carbon: -0.239

Hydrogen: 0.239
|Nitrogen: -1.102

Boron: 0.747

Hydrogen (bonded to N): 0.432

Hydrogen (bonded to B): -0.077
|-
!Discussion
|From the visualisation, it is shown that there is a slightly negative charge on the carbon atoms, and a positive charge of the same magnitude on the hydrogen atoms. All the carbon atoms have the same charge as they are in identical environments. The same applies to all the hydrogen atoms. This is due to the highly symmetrical structure of benzene. Since the same colour scale was used for both benzene and borazine, and the charges are much smaller in magnitude on atoms in benzene than atoms on borazine, the colours on the charge distribution visualisation is much darker.
|#explain
|}

===Comparative MOs of Benzene and Borazine===

{| class="wikitable"
!
!Benzene
!Borazine
!Comparison and Discussion
|-
!1st comparative pair
|[[File:Hyc116_benzene_1st_MO_pair_7.png|200x200px|centre]]
|[[File:Hyc116_borazine_1st_MO_pair_level9.png|200x200px|centre]]
|MO 9 of both benzene and borazine are comparable.
|-
!2nd comparative pair
|[[File:Hyc116_benzene_2nd_MO_pair_10.png|200x200px|centre]]
|[[File:Hyc116_borazine_2nd_MO_pair_level11.png|200x200px|centre]]
|
|-
!3rd comparative pair
|[[File:Hyc116_benzene_3rd_MO_pair_21.png|200x200px|centre]]
|[[File:Hyc116_borazine_3rd_MO_pair_level21.png|200x200px|centre]]
|
|}

===Aromaticity: some theories===

==Reference==

MO hyc116

2018-05-24T15:54:32Z

Hyc116: /* Charge distribution */

==BH3==

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_bh3_631g_opt_summarytable.png]]

The above summary table was obtained after the 2nd optimisation of BH3 (after the initial optimisation using the 3-21G basis set). Notice how the symmetry is incorrect and shown as Cs. This is because the symmetry was manually broken at the beginning by changing the bond length of B-H bonds. The point group was manually adjusted and the molecule was optimised again before the frequency analysis and the new summary table is attached below.

[[file:Hyc116_bh3_correctsummarytable.png]]

The above summary table was obtained from the optimisation after adjusting the symmetry. The point shown in this summary table is D3h, which is the correct for BH3.

'''Items table'''

Below is the items table taken from the optimisation with the correct point group.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116 BH3 FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

'''jmol of BH3'''
<jmol><jmolApplet>
<title>optimised BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum===

{| class="wikitable"
!wavenumber (cm-1)
!Intensity (arbitrary units)
!symmetry
!IR active?
!type
|-
|1163
|93
|A2' '
|Yes
|Out of plane bend
|-
|1213
|14
|E'
|Very slight
|Bend
|-
|1213
|14
|E'
|Very slight
|Bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|-
|2716
|126
|E'
|Yes
|Asymmetric stretch
|}

'''IR spectrum'''

[[file:Hyc116_ir_bh3.png|400*600]]

There are only three peaks on the IR spectrum of BH3, despite that there are 6 vibrational modes for the molecule. As shown in the table above, the symmetric stretching mode with A1 symmetry at 2582 cm-1 is not IR active; naturally, that vibrational mode doesn’t give a peak on the IR spectrum. As shown from the table, two pairs of vibrational modes, the bond angle deformation/bend at 1213 cm-1 and the asymmetric bond stretch at 2716 cm-1, are degenerate with the symmetry label E. This means that they have the same energy, and hence give the same wavenumber on the IR spectrum. Each pair of degenerate vibrational modes give rise to one peak. This leaves three peaks, as confirmed by the IR spectrum above.

===Molecular orbitals of BH3===

[[file:hyc116_bh3_MO_diagram.png]]

The above molecular orbital diagram was taken from Dr Patricia Hunt's Lecture 4 Tutorial Problem Model Answers. <ref>P. Hunt, "Lecture 4 Tutorial Problem Model Answers", 2 (2018)</ref>. Diagrams of the "real" MOs were obtained from Gaussian.

There is no significant difference between the LCAO MOs and the real ones. Features such as orbital phases are shown clearly on both the LCAO MOs and the real MOs, illustrating the bonding/anti-bonding characters of the molecular orbitals. This suggests that the the qualitative MO theory is highly accurate and useful when studying the molecular orbitals of molecules.

==Associated energies: ammonium borane==

===NH3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_nh3_631g_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_NH3_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

'''jmol of NH3'''
<jmol><jmolApplet>
<title>optimised NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_nh3bh3_631g_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000515 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_NH3BH3_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -0.0014 -0.0011 -0.0006 6.9624 20.4518 43.5542
Low frequencies --- 266.4530 632.2458 639.0504
</pre>

'''jmol of NH3BH3'''
<jmol><jmolApplet>
<title>optimised NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association energy===

E(BH3) (using the optimisation with the correct symmetry) = -26.61532363 a.u. = -26.61532 a.u. (5 d.p.)

E(NH3) = -56.55776873 a.u. = -56.55777 a.u. (5 d.p.)

E(NH3BH3) = -83.22468893 a.u. = -83.22469 a.u. (5 d.p.)

Carrying out calculations using numbers which has already been rounded up can possibly result in errors in the last digit. Hence, here the calculations were carried out using the numbers provided from the optimisations (i.e. with more decimal places than necessary); the answer was then rounded up to the desired accuracy.

ΔE = E(NH3BH3)-[E(NH3)+E(BH3)]

ΔE = -83.22468893 - (-56.55776873 + -26.61532363) = -0.05159657 a.u.

ΔE = -0.05160 a.u. (5 d.p.)

'''Converting energy from a.u. to kJ/mol'''
An atomic unit for energy is Hartree, which is equal to 2625.5 kJ/mol. <ref>https://cccbdb.nist.gov/hartree.asp (Accessed: 22.05.2018)</ref>

So ΔE in kJ/mol = -0.05159657 * 2625.5 = -135.466794535 kJ/mol

ΔE = -135 kJ/mol (nearest integer)

The energy difference calculated above comes from the formation of the B-N dative bond. It is a relatively weak bond. According to a bond energy data sheet provided by the University of California, <ref>https://labs.chem.ucsb.edu/zakarian/armen/11---bonddissociationenergy.pdf (Accessed on 24.05.2018)</ref> the bond energy of the C-C bond of an ethane molecule is 368 kJ/mol. This is a fair comparison to the NH3BH3 molecule as the two molecules have the same structure, only with the carbon atoms on ethane swapped for Boron and Nitrogen in NH3BH3

==Using a mixture of basis-sets and pseudo-potentials==

===BBr3===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: Boron: 6-31G(d,p) ; Br: LANL2DZ

'''Summary table'''

[[file:Hyc116_bbr3_opt_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:Hyc116_bbr3_freq.log]]

Attached above is the frequency file saved onto the computer from the SCAN server portal. The frequency file was also published on the chemistry database DSpace. {{DOI|10042/202442}}

'''Frequencies'''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''jmol of BBr3'''
<jmol><jmolApplet>
<title>optimised BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Hyc116_bbr3_freq.log</uploadedFileContents>
</jmolApplet></jmol>

==Aromaticity==

===Benzene===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_c6h6_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.000830 0.001800 YES
RMS Displacement 0.000294 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_C6H6_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -3.5606 -3.5606 -0.0089 -0.0043 -0.0043 10.0905
Low frequencies --- 413.9582 413.9582 621.1416
</pre>

'''jmol of C6H6'''
<jmol><jmolApplet>
<title>optimised Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_C6H6_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Borazine===

Calculation type: Optimisation

Calculation Method: B3LYP

Basis set: 6-31G(d,p)

'''Summary table'''

[[file:Hyc116_borazine_summarytable.png]]

'''Items table'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000250 0.001800 YES
RMS Displacement 0.000074 0.001200 YES
</pre>

'''Frequency log file'''

[[Media:HYC116_BORAZINE_FREQ.LOG]]

'''Frequencies'''

<pre>
Low frequencies --- -12.6626 -12.6626 -8.9272 -0.0211 -0.0104 -0.0104
Low frequencies --- 289.1112 289.1112 403.8613
</pre>

'''jmol of Borazine'''
<jmol><jmolApplet>
<title>optimised Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HYC116_BORAZINE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Charge distribution===

An NBO charge analysis was carried out on both the optimised benzene and borazine. Visualisations of the charge distribution are shown in the table below, with the colour range going from -1.102 to 1.102 for both molecule. This large scale was chosen as it allows direct comparison of the charge on any atoms in these two molecules and shows the relative magnitude of charges on all these atoms. Negative charges are shown in red, and positive charges are shown in green. A neutral charge is displayed in black, so the smaller a charge is (positive or negative), the darker its colour representation is. Larger charges are shown in brighter colours. The charges are also displayed on the atoms as numbers with a neutral charge being zero. Negative charges are shown as negative number and positive charges are shown as positive numbers.

{| class="wikitable"
!
!Benzene
!Borazine
|-
!Visualisation of charge distribution
|[[File:Hyc116_benzene_charge_distribution1.png|500x500px|thumb|centre|Charge distribution of Benzene visualisation]]
|[[File:Hyc116_borazine_charge_distribution1.png|500x500px|thumb|centre|Charge distribution of Borazine visualisation]]
|-
!Charge
|Carbon: -0.239

Hydrogen: 0.239
|Nitrogen: -1.102

Boron: 0.747

Hydrogen (bonded to N): 0.432

Hydrogen (bonded to B): -0.077
|-
!Discussion
|From the visualisation, it is shown that there is a slightly negative charge on the carbon atoms, and a positive charge of the same magnitude on the hydrogen atoms. All the carbon atoms have the same charge as they are in identical environments. The same applies to all the hydrogen atoms. This is due to the highly symmetrical structure of benzene. Since the same colour scale was used for both benzene and borazine, and the charges are much smaller in magnitude on atoms in benzene than atoms on borazine, the colours on the charge distribution visualisation is much darker.
|#explain
|}

===Comparative MOs of Benzene and Borazine===

{| class="wikitable"
!
!Benzene
!Borazine
!Comparison and Discussion
|-
!1st comparative pair
|[[File:Hyc116_benzene_1st_MO_pair_7.png|200x200px|centre]]
|[[File:Hyc116_borazine_1st_MO_pair_level9.png|200x200px|centre]]
|
|-
!2nd comparative pair
|[[File:Hyc116_benzene_2nd_MO_pair_10.png|200x200px|centre]]
|[[File:Hyc116_borazine_2nd_MO_pair_level11.png|200x200px|centre]]
|
|-
!3rd comparative pair
|[[File:Hyc116_benzene_3rd_MO_pair_21.png|200x200px|centre]]
|[[File:Hyc116_borazine_3rd_MO_pair_level21.png|200x200px|centre]]
|
|}

===Aromaticity: some theories===

==Reference==