ChemWiki - User contributions [en]

Rep:Mod:cel16inorganic

2018-05-25T14:35:33Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, illustrating the importance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The difference between charges on the atoms in benzene is much smaller than in borazine, illustrating that although the two structures are isoelectric, their relative charge distributions differ. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is seen by the electronic distribution over the C-H bonds of benezene. Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative, this magnitude is greater than the negative charge of the hydrogen atoms bonded to B due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both have 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both. All the C-H σ bonding orbitals appear to be in phase with the out-of-phase interaction seen in the centre of the ring. The bonding interaction seems to be from the interaction of a C sp2-orbital with a 1s H orbital.

MO 12 from benzene is highly symmetric, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 alternating, in-phase and out-of-phase C-C interactions with no hydrogen interactions in either, corresponding to the formation of σ C-C bonds. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz orbital is donated to form a delocalised π system above the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz atomic orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals. This definition of aromaticity also fails to explain more complex aromatic systems, which involve donation of electron density from orbitals which don't have the same symmetry as the Pz orbital, this is due to the fact that the original definition of aromaticity is based purely on benzene.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-25T14:33:43Z

Cel16: /* MO analysis */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, illustrating the importance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The difference between charges on the atoms in benzene is much smaller than in borazine, illustrating that although the two structures are isoelectric, their relative charge distributions differ. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is seen by the electronic distribution over the C-H bonds of benezene. Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative, this magnitude is greater than the negative charge of the hydrogen atoms bonded to B due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both have 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both. All the C-H σ bonding orbitals appear to be in phase with the out-of-phase interaction seen in the centre of the ring. The bonding interaction seems to be from the interaction of a C sp2-orbital with a 1s H orbital.

MO 12 from benzene is highly symmetric, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 alternating, in-phase and out-of-phase C-C interactions with no hydrogen interactions in either, corresponding to the formation of σ C-C bonds. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz orbital is donated to form a delocalised π system above the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals. This definition of aromaticity also fails to explain more complex aromatic systems, which involve donation of electron density from orbitals which don't have the same symmetry as the Pz orbital, this is due to the fact that the original definition of aromaticity is based purely on benzene.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-25T14:33:28Z

Cel16: /* MO analysis */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, illustrating the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The difference between charges on the atoms in benzene is much smaller than in borazine, illustrating that although the two structures are isoelectric, their relative charge distributions differ. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is seen by the electronic distribution over the C-H bonds of benezene. Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative, this magnitude is greater than the negative charge of the hydrogen atoms bonded to B due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both have 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both. All the C-H σ bonding orbitals appear to be in phase with the out-of-phase interaction seen in the centre of the ring. The bonding interaction seems to be from the interaction of a C sp2-orbital with a 1s H orbital.

MO 12 from benzene is highly symmetric, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 alternating, in-phase and out-of-phase C-C interactions with no hydrogen interactions in either, corresponding to the formation of σ C-C bonds. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz orbital is donated to form a delocalised π system above the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals. This definition of aromaticity also fails to explain more complex aromatic systems, which involve donation of electron density from orbitals which don't have the same symmetry as the Pz orbital, this is due to the fact that the original definition of aromaticity is based purely on benzene.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-25T14:32:23Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The difference between charges on the atoms in benzene is much smaller than in borazine, illustrating that although the two structures are isoelectric, their relative charge distributions differ. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is seen by the electronic distribution over the C-H bonds of benezene. Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative, this magnitude is greater than the negative charge of the hydrogen atoms bonded to B due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both have 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both. All the C-H σ bonding orbitals appear to be in phase with the out-of-phase interaction seen in the centre of the ring. The bonding interaction seems to be from the interaction of a C sp2-orbital with a 1s H orbital.

MO 12 from benzene is highly symmetric, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 alternating, in-phase and out-of-phase C-C interactions with no hydrogen interactions in either, corresponding to the formation of σ C-C bonds. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz orbital is donated to form a delocalised π system above the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals. This definition of aromaticity also fails to explain more complex aromatic systems, which involve donation of electron density from orbitals which don't have the same symmetry as the Pz orbital, this is due to the fact that the original definition of aromaticity is based purely on benzene.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-25T14:29:23Z

Cel16: /* Computed molecular orbital analysis and comparison */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The difference between charges on the atoms in benzene is much smaller than in borazine, illustrating that although the two structures are isoelectric, their relative charge distributions differ. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is seen by the electronic distribution over the C-H bonds of benezene. Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative, this magnitude is greater than the negative charge of the hydrogen atoms bonded to B due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both have 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both. All the C-H σ bonding orbitals appear to be in phase with the out-of-phase interaction seen in the centre of the ring. The bonding interaction seems to be from the interaction of a C sp2-orbital with a 1s H orbital.

MO 12 from benzene is highly symmetric, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 alternating, in-phase and out-of-phase C-C interactions with no hydrogen interactions in either, corresponding to the formation of σ C-C bonds. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals. This definition of aromaticity also fails to explain more complex systems, which involve donation of electron density from orbitals which don't have the same symmetry as the Pz orbital. This is due to the fact that the original definition of aromaticity is based purely on benzene.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-25T14:19:35Z

Cel16: /* Charge distribution comparison */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The difference between charges on the atoms in benzene is much smaller than in borazine, illustrating that although the two structures are isoelectric, their relative charge distributions differ. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is seen by the electronic distribution over the C-H bonds of benezene. Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative, this magnitude is greater than the negative charge of the hydrogen atoms bonded to B due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals. This definition of aromaticity also fails to explain more complex systems, which involve donation of electron density from orbitals which don't have the same symmetry as the Pz orbital. This is due to the fact that the original definition of aromaticity is based purely on benzene.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:41:05Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals. This definition of aromaticity also fails to explain more complex systems, which involve donation of electron density from orbitals which don't have the same symmetry as the Pz orbital. This is due to the fact that the original definition of aromaticity is based purely on benzene.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:31:38Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:30:59Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).
With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Jug, K. and Koster, A. M. (1990) ‘Influence of. sigma. and. pi. electrons on aromaticity’, J. Am. Chem. Soc., 112(6), pp. 6772–6777. doi: 10.1021/ja00175a005.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:27:05Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).
With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref name=":0" />. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:25:55Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).
With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref name=":1" />. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pz orbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:25:07Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).
With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref name=":0" />. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pzorbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:22:35Z

Cel16:

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).
With benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C σ bonds and one C-H σ bond. The leftover unpaired electron in the Pz is donated to form a delocalised π system in the plane of the ring. This structure goes some way to explaining the reactivity of benzene and other aromatic systems. However, studies have shown that the σ bonding system may have a role to play in the stability of the aromatic system<ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. This would negate the idea that the only contribution into the delocalised system comes form the crossover of orthogonal Pzorbitals. The MO analysis shown above for the π bonding molecular orbital seems to indicate that there may be contributions of electron density from other orbitals.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:06:56Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).
In benzene it has be proposed that the ring is formed of six sp2 hybridised Cs, which each form two C-C bonds and one C-H bond. The leftover occupied Pz

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T22:01:33Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules<ref>Kikuchi, S. (1997) ‘A History of the Structural Theory of Benzene - The Aromatic Sextet Rule and Huckel’s Rule’, Journal of Chemical Education, 74(2), p. 194. doi: 10.1021/ed074p194.</ref>). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds. A ring current can also be induced if the system is placed in an external magnetic field, this causes the shielding of the inner protons in 1H NMR. Due to their increased stability, when undergoing reactions it is often favourable for the aromatic ring to remain intact therefore, they tend to undergo aromatic substitution (instead of e.g. addition).

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T21:51:15Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules). This increases the stability of the system to be greater than their olefinic equivalents <ref>Palusiak, M. and Krygowski, T. M. (2007) ‘Application of AIM parameters at ring critical points for estimation of π-electron delocalization in six-membered aromatic and quasi-aromatic rings’, Chemistry - A European Journal, 13(28), pp. 7996–8006. doi: 10.1002/chem.200700250.</ref>. The bond lengths of within aromatic systems are at an intermediate length between the shorter, unsaturated bonds and longer saturated bonds.

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T21:45:17Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==
Aromaticity can be observed in planar, ring-systems exhibiting unsaturation which allows the formation of resonance forms (obeying Hückel's rules). This increases the stability of the system to be greater than their olefinic equivalents. The bond lengths

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:55:43Z

Cel16: /* Computed molecular orbital analysis and comparison */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present.
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:55:22Z

Cel16:

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to. There also appears to be an interaction/overlap of electron density with some of the hydrogens present
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:53:07Z

Cel16: /* Optimisation and frequency analysis */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

<jmol><jmolApplet>
<title>Borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL16 BORAZINE FREQ D3H.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:52:25Z

Cel16: /* Optimisation and frequency analysis */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

<jmol><jmolApplet>
<title>Benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>BENZENE OPT CEL16 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

'''JMOL'''

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:51:51Z

Cel16: /* BBr3 */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Cel16_BBr3_opt_comp_freq_1.log </uploadedFileContents>
</jmolApplet></jmol>

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

'''JMOL'''

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

'''JMOL'''

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:51:14Z

Cel16:

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3 molecule:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL_NH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_CEL16.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

'''''JMOL'''''

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

'''JMOL'''

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

'''JMOL'''

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:49:47Z

Cel16: /* Optimisation and frequency analysis */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

Optimised BH3:
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CEL BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

'''''JMOL'''''

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

'''''JMOL'''''

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

'''''JMOL'''''

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

'''JMOL'''

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

'''JMOL'''

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:48:13Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

'''''INSERT JMOL'''''

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

'''''JMOL'''''

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

'''''JMOL'''''

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

'''''JMOL'''''

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

'''JMOL'''

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

'''JMOL'''

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase C-C interactions with no hydrogen interactions in either. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:43:17Z

Cel16: /* Computed molecular orbital analysis and comparison */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

'''''INSERT JMOL'''''

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

'''''JMOL'''''

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

'''''JMOL'''''

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

'''''JMOL'''''

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

'''JMOL'''

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

'''JMOL'''

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond. This is stabilising effect is likely why this specific MO for borazine is lower in energy than the corresponding MO for benzene.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|These MOs appear to have equal antibonding and bonding characteristics. With both having a very similar shape resulting from 3 in-phase and out-of-phase interactions. The benzene MO is slightly more stabilised. This may be because the large electronegativity differences between the cyclic atoms in borazine do not favour a symmetric arrangement.

|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Both of these MOs correspond to the LUMO. They represent the highest energy pi bonding interaction present in both molecules, consisting of two in-phase interactions on opposite sides of the molecule. The MO from benzene is more symmetric as no polarisation of the MO occurs. However, the MO from borazine has a larger area of electron density focused on the N-B-N interaction, than the B-N-B interaction. This is likely due to nitrogen's greater electronegativity which draws electron density away from the two boron and one hydrogen atom they're bonded to.
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:23:53Z

Cel16: /* Computed molecular orbital analysis and comparison */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

'''''INSERT JMOL'''''

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

'''''JMOL'''''

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

'''''JMOL'''''

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

'''''JMOL'''''

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

'''JMOL'''

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

'''JMOL'''

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three π MOs, 12 σ MOs, and 6 core non bonding orbitals. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10|287x287px]]
|The following MOs show antibonding C-C character, with a nodal plane along each of the C-C bonds. However, C-H bonding is present in both.

MO 12 from benzene is highly symmetrical, with bonding visible between each carbon and its corresponding hydrogen. A bonding interaction between all the Hs is also visible. This is not present in the borazine which is much less symmetric. The hydrogen atoms adjacent to the Boron atoms aren't seen to interact. The bonding interactions between the nitrogen and their adjacent hydrogens are much more electron dense than the C-H interaction in benzene. This is probable due to nitrogen's greater electron density/electronegativity. Resulting in a more polarised bond.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|278x278px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|276x276px]]
|Bonding (σ)

Both of these MOs correspond to 3 in-phase and 3 out-of-phase interactions,
|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|291x291px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|288x288px|Molecular orbital 21]]
|Bonding (π)
|}

== Aromaticity ==

= References =
<references />

Rep:Mod:cel16inorganic

2018-05-24T19:00:06Z

Cel16: /* Aromaticity */

__TOC__

= Part 1 =

== BH3 ==

=== Optimisation and frequency analysis ===
A BH3 molecule was optimised:

B3LYP/6-31G(d,p)
[[File:Cel summary BH3.PNG|none|thumb|300x300px|Summary table for optimised BH3 molecule.]]

The item table below illustrates that the optimisation was successful by showing (along with the RMS gradient <0.001 AU) that convergence was achieved:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000196 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

The frequency analysis of the optimised BH3 yielded the zero frequencies shown below. These correspond to an optimised (minimum) structure:

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0056 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

Frequency analysis file: [[media:CEL BH3 FREQ.LOG|CEL BH3 FREQ.LOG]]

'''''INSERT JMOL'''''

=== Vibration analysis ===
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|Yes
|Out-of-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|1213
|14
|E'
|V. Slightly
|In-plane bend
|-
|2582
|0
|A1'
|No
|Symmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|-
|2715
|126
|E'
|Yes
|Asymmetric stretch
|}
[[File:Cel16 IR spectrum BH3.PNG|none|thumb|Calculated IR spectrum of optimised BH3|502x502px]]

Only three IR peaks are observed for BH3 rather than the six stretch/bend modes which can occur (as predicted by the 3N-6 rule)<ref>Coates, J. (2006) ‘Interpretation of Infrared Spectra, A Practical Approach’, in ''Encyclopedia of Analytical Chemistry''. doi: 10.1002/9780470027318.a5606.</ref>. This is due to the degeneracy of the two asymmetric stretches and the two in-plane bends, in addition to the IR inactive symmetric stretch. Degenerate signals occur at the same wavenumber and intensity so are superimposed on the IR spectrum, causing only a single peak to be observed.
=== MO analysis ===
[[File:MO BH3 cel16.jpeg|none|thumb|638x638px|Molecular orbital diagram of BH3 showing LCAOs and computed MOs.(inspired by diagram by P.Hunt <ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf , (Accessed, May 2018)</ref>) ]]In most cases, the LCAOs appear to be very similar to the computed MOs, with the same basic symmetry and geometry. However, the antibonding ''3a1'<nowiki/>'' computed MO appears to have less antibonding character than the corresponding LCAO, seen by the larger area of electron density surrounding the central boron atom . This may mean that the ''3a1''' MO is slightly more stabilised than is indicated in the diagram. Overall, the LCAOs are a good representation of the computed MOs, this illustrates the significance of molecular orbital theory in predicting the shape of real MOs.

== NH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3 summary CEL.JPG|none|thumb|324x324px|Summary table for optimised NH3 ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000348 0.000450 YES
RMS Force 0.000256 0.000300 YES
Maximum Displacement 0.005481 0.001800 NO
RMS Displacement 0.002707 0.001200 NO
</pre>

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

Frequency analysis file: [[media:CEL NH3 OPT FREQ.LOG|CEL NH3 OPT FREQ.LOG]]

Optimised NH3 molecule:

'''''JMOL'''''

== NH3BH3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised NH3BH3 molecule:

B3LYP/6-31G(d,p)
[[File:NH3BH3 summary CEL.JPG|none|thumb|323x323px|Summary table for optimised NH3BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

<pre>
Low frequencies --- 0.0008 0.0010 0.0012 18.0575 28.4116 40.0963
Low frequencies --- 266.4888 632.3850 639.5950
</pre>

Frequency analysis file: [[media:NH3BH3 FREQ CEL16.LOG|NH3BH3 FREQ CEL16.LOG]]

Optimised NH3BH3 molecule:

'''''JMOL'''''

=== Association/dissociation Energy calculation ===
{| class="wikitable"
!Molecular fragment
!Energy, E(RB3LYP) (au)
|-
|BH3
|<nowiki>-26.61533</nowiki>
|-
|NH3
|<nowiki>-56.55777</nowiki>
|-
|NH3BH3
|<nowiki>-83.22469</nowiki>
|}
Using the equation: ''ΔE=E(NH3BH3)-[E(NH3)+E(BH3)], ''the dissociation and association energies of the B-N bond in ammonia-borane can be calculated<ref>Hunt research group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/9a_bh3nh3_energy.html , (Accessed, May 2018)</ref>.
{| class="wikitable"
!ΔE(RB3LYP)
!au
!KJ mol-1
|-
|Association Energy
|<nowiki>-0.0516</nowiki>
|<nowiki>-135</nowiki>
|-
|Dissociation Energy
|<nowiki>+0.0516</nowiki>
|<nowiki>+135</nowiki>
|}
The association energy was calculated using the equation above as this corresponds to the forward reaction i.e. formation of ammonia-borane from ammonia and borane. From this the dissociation energy was calculated. It has the same magnitude as the association energy, with a positive energy change. When comparing with the covalent C-H bond in methane, which has an dissociation energy of +438.892 KJ mol-1, the dissociation energy of the N-B bond in ammonia-borane is relatively low. This suggests that the dative bond is weak. This may be due to the greater electronegativity of the nitrogen, which makes it a weak electron donor destabilising the dative bond<ref>Ruscic, B. (2015) ‘Active Thermochemical Tables: Sequential Bond Dissociation Enthalpies of Methane, Ethane, and Methanol and the Related Thermochemistry’, ''Journal of Physical Chemistry A'', 119(28), pp. 7810–7837. doi: 10.1021/acs.jpca.5b01346.</ref>.

== BBr3 ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised BBr3 molecule:

B3LYP/6-31G(d,p), pseudo-potential: LANL2DZ
[[File:BBr3 summary cel16.JPG|none|thumb|Summary table for optimised BBr3|308x308px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

<pre>
Low frequencies --- -1.9018 -0.0001 -0.0001 0.0002 1.5796 3.2831
Low frequencies --- 155.9053 155.9625 267.7047
</pre>

Frequency analysis file: [[media:Cel16 BBr3 opt comp freq 1.log|Cel16 BBr3 opt comp freq 1.log]]

Frequency file of successful analysis on Dspace:{{DOI|10042/202452}}

Optimised BBr3 molecule:

'''''JMOL'''''

= Part 2 (Aromaticity) =

== Benzene ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised benzene molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 benzene summary D6H.JPG|none|thumb|385x385px|Summary table for optimised benzene]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0044 -0.0044 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

Frequency analysis file: [[media:BENZENE OPT CEL16 FREQ.LOG|BENZENE OPT CEL16 FREQ.LOG]]

Optimised benzene molecule:

'''JMOL'''

== Borazine ==

=== Optimisation and frequency analysis ===
The summary, item table and zero frequencies shown below illustrate that the optimisation was successful and convergence was achieved for the optimised borazine molecule:

B3LYP/6-31G(d,p)
[[File:Cel16 borazine summary D3H.JPG|none|thumb|312x312px|Summary table for optimised borazine]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000248 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
</pre>

<pre>
Low frequencies --- -6.8949 -6.2722 -5.8025 -0.0107 0.0583 0.1547
Low frequencies --- 289.2034 289.2114 403.7636
</pre>

Frequency analysis file: [[media:CEL16 BORAZINE FREQ D3H.LOG|CEL16 BORAZINE FREQ D3H.LOG]]

Optimised borazine molecule:

'''JMOL'''

== Charge distribution comparison ==
Using NBO with colour range: -0.900 to 0.900
{| class="wikitable"
!Benzene
!Borazine
|-
|[[File:Cel16 benzene chargeno.JPG|thumb|333x333px|none]]
|[[File:Cel16 borazine chargeno.JPG|thumb|314x314px|none]]
|-
|Charge on carbon: -0.238
|Charge on nitrogen:-1.102
Charge on boron:+0.747
|-
|Charge on hydrogen: +0.239
|Charge on hydrogen adjacent to N: +0.432
Charge on hydrogen adjacent to B: -0.077
|}
The differences in charges for the atoms in benzene is much less than in borazine, showing that although the two structures are isoelectric, their relative charge distributions differ greatly. Carbon has an electronegativity of 2.5<ref name=":0">Allred, A. L. and Rochow, E. G. (1958) ‘A scale of electronegativity based on electrostatic force’, ''Journal of Inorganic and Nuclear Chemistry''. Pergamon Press Ltd, 5(4), pp. 264–268. doi: 10.1016/0022-1902(58)80003-2.</ref> (based on the Pauling scale) which is slightly higher than that of hydrogen, 2.2. This is illustrated in the electronic distribution benzene, as Carbon has a small negative charge (-0.238) as it draws electron density towards itself and hydrogen has the corresponding positive charge (+0.239) as electron density is drawn away from its centre. The charges balance as overall the molecule has no net charge.

In the case of borazine, the charge distribution is less symmetric as not all the hydrogens are equivalent. The bonding in borazine is aromatic however, it has more ionic character than the bonding in benzene. This is due to the greater difference in electronegativity between the nitrogen and boron atoms<ref>L. F, H. and G. W, S. (1961) ‘Borazine Chemistry’, in ''BORAX TO BORANES'', pp. 232–240. doi: doi:10.1021/ba-1961-0032.ch026\r10.1021/ba-1961-0032.ch026.</ref>. The electronegativity of nitrogen is 3.0 compared with 2.0 for boron therefore, in this system the relative electronegativities are: N>H>B<ref name=":0" />. This explains why N has the greatest negative charge (-1.102), as it is the most effective at drawing electron density towards its centre, the opposite is true for boron which has the greatest positive charge (+0.747) due to its electron deficiency. The hydrogen atoms bonded to boron exhibit a slightly negative charge, as H is more electronegative than B. Whereas, the hydrogen atoms bonded to nitrogen have a positive charge as nitrogen is more electronegative than them, this magnitude is great than the negative charge of the other hydrogen atoms due to the greater difference in electronegativity between H and N. Overall the charges balance as borazine has no net charge.

== Computed molecular orbital analysis and comparison ==
Benzene and borazine both had 21 filled molecular orbitals consisting of: three bonding π MOs, nine bonding σ MOs and 3 antibonding σ* MOs. Although the combination of filled orbitals was the same, the size and relative energies of those orbitals differed:
{| class="wikitable"
!Computed benzene MO
!Computed borazine MO
!Comparison
|-
|[[File:Cel16 benzene MO12.JPG|none|thumb|305x305px|Molecular orbital 12]]
|[[File:Cel16 borazine MO10.JPG|none|thumb|Molecular orbital 10]]
|Antibonding (σ*)The following MOs are both filled σ* orbitals with relatively low energies. MO 12 from benzene is highly symmetrical out of phase arrangement, with none of the electron density

The borazine is much less symmetric. The out-of-phase centre is larger and significantly smaller electron density is donated from the boron.
|-
|[[File:Cel16 benzene MO14.JPG|none|thumb|Molecular orbital 14|256x256px]]
|[[File:Cel16 borazine MO15.JPG|none|thumb|Molecular orbital 15|258x258px]]
|Bonding (σ)

Both of these MOs correspond to 3 in-phase and 3 out-of-phase interactions
|-
|[[File:Cel16 benzene MO21.JPG|none|thumb|279x279px|Molecular orbital 21]]
|[[File:Cel16 borazine MO21.JPG|none|thumb|269x269px|Molecular orbital 21]]
|Bonding (π)
|}

== Aromaticity ==

= References =
<references />

File:Cel16 benzene MO12.JPG

2018-05-24T18:48:36Z

Cel16:

File:Cel16 borazine MO10.JPG

2018-05-24T18:47:40Z

Cel16:

File:Cel16 borazine MO21.JPG

2018-05-24T18:20:52Z

Cel16:

File:Cel16 benzene MO21.JPG

2018-05-24T18:19:36Z

Cel16:

File:Cel16 benzene MO20.JPG

2018-05-24T17:58:20Z

Cel16:

File:Cel16 borazine MO20.JPG

2018-05-24T17:56:12Z

Cel16:

Rep:Mod:cel16inorganic

2018-05-24T17:38:54Z

Cel16: /* Computed molecular orbital analysis and comparison */

File:Cel16 borazine MO17.JPG

2018-05-24T17:28:35Z

Cel16:

Rep:Mod:cel16inorganic

2018-05-24T17:25:37Z

Cel16: /* Computed molecular orbital analysis and comparison */

File:Cel16 borazine MO15.JPG

2018-05-24T17:25:26Z

Cel16: Cel16 uploaded a new version of File:Cel16 borazine MO15.JPG

File:Cel16 borazine MO15.JPG

2018-05-24T17:23:32Z

Cel16:

File:Cel16 borazine MO16.JPG

2018-05-24T17:21:58Z

Cel16:

File:Cel16 benzene MO17.JPG

2018-05-24T17:20:16Z

Cel16:

File:Cel16 benzene MO14.JPG

2018-05-24T17:17:52Z

Cel16:

File:Cel16 benzene MO13.JPG

2018-05-24T17:16:46Z

Cel16:

Rep:Mod:cel16inorganic

2018-05-24T16:46:52Z

Cel16: /* MO analysis */

Rep:Mod:cel16inorganic

2018-05-24T16:29:50Z

Cel16:

Rep:Mod:cel16inorganic

2018-05-24T16:03:04Z

Cel16: /* Computed molecular orbital analysis and comparison */

Rep:Mod:cel16inorganic

2018-05-24T15:56:43Z

Cel16: /* References */

Rep:Mod:cel16inorganic

2018-05-24T15:55:31Z

Cel16: /* References */

Rep:Mod:cel16inorganic

2018-05-24T15:53:52Z

Cel16: /* Optimisation and frequency analysis of borazine */

File:Cel16 benzene chargeno.JPG

2018-05-24T15:17:08Z

Cel16: