ChemWiki - User contributions [en]

All Hail The Return Of GaussView

2018-05-18T15:24:31Z

Pg1716: /* BBr3 */

=== Introduction ===
GaussView makes its much anticipated return in 2018 with its biggest assignment yet...

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/ B: 6-31G (d,p) Br: LANL2DZ'''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p)'''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparison of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

<div id="Delocalised pz">
[[File:P_delocalised_Gobbett.png|frameless|500px|centre]]
</div>

However, MO calculations show that this is not the sole bonding orbital and that there are many MOs of similar energy that have sigma character. This suggests that the view that aromaticity is defined by solely by orthogonal p<sub>z</sub> orbitals is flawed and that the real picture is far more complex. An example is included below, in which the MO has sigma character, but still represents a bonding orbital in which the electrons are delocalised (the nodes are atom-based and the MO is cyclic). This MO is formed from p-orbitals in the plane of the ring showing an effect known as σ-aromaticity. Thus, clearly, MO theory has shown that the Huckel view of aromaticity is not complete.

<div id="Delocalised sigma">
[[File:MO14_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]

[REF: L. ZH; ''et al'', ''Sigma-aromaticity and sigma-antiaromaticity in saturated inorganic rings'', J Phys Chem, 2005, 109, 16, 3711-3716]

[REF: S. Hadlington, ''Elusive σ aromaticity captured'', Chemistry World, 2014]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T15:24:09Z

Pg1716: /* Borazine */

=== Introduction ===
GaussView makes its much anticipated return in 2018 with its biggest assignment yet...

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p)'''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparison of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

<div id="Delocalised pz">
[[File:P_delocalised_Gobbett.png|frameless|500px|centre]]
</div>

However, MO calculations show that this is not the sole bonding orbital and that there are many MOs of similar energy that have sigma character. This suggests that the view that aromaticity is defined by solely by orthogonal p<sub>z</sub> orbitals is flawed and that the real picture is far more complex. An example is included below, in which the MO has sigma character, but still represents a bonding orbital in which the electrons are delocalised (the nodes are atom-based and the MO is cyclic). This MO is formed from p-orbitals in the plane of the ring showing an effect known as σ-aromaticity. Thus, clearly, MO theory has shown that the Huckel view of aromaticity is not complete.

<div id="Delocalised sigma">
[[File:MO14_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]

[REF: L. ZH; ''et al'', ''Sigma-aromaticity and sigma-antiaromaticity in saturated inorganic rings'', J Phys Chem, 2005, 109, 16, 3711-3716]

[REF: S. Hadlington, ''Elusive σ aromaticity captured'', Chemistry World, 2014]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T15:18:25Z

Pg1716: /* Introduction */

=== Introduction ===
GaussView makes its much anticipated return in 2018 with its biggest assignment yet...

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparison of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

<div id="Delocalised pz">
[[File:P_delocalised_Gobbett.png|frameless|500px|centre]]
</div>

However, MO calculations show that this is not the sole bonding orbital and that there are many MOs of similar energy that have sigma character. This suggests that the view that aromaticity is defined by solely by orthogonal p<sub>z</sub> orbitals is flawed and that the real picture is far more complex. An example is included below, in which the MO has sigma character, but still represents a bonding orbital in which the electrons are delocalised (the nodes are atom-based and the MO is cyclic). This MO is formed from p-orbitals in the plane of the ring showing an effect known as σ-aromaticity. Thus, clearly, MO theory has shown that the Huckel view of aromaticity is not complete.

<div id="Delocalised sigma">
[[File:MO14_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]

[REF: L. ZH; ''et al'', ''Sigma-aromaticity and sigma-antiaromaticity in saturated inorganic rings'', J Phys Chem, 2005, 109, 16, 3711-3716]

[REF: S. Hadlington, ''Elusive σ aromaticity captured'', Chemistry World, 2014]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T15:16:27Z

Pg1716:

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparison of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

<div id="Delocalised pz">
[[File:P_delocalised_Gobbett.png|frameless|500px|centre]]
</div>

However, MO calculations show that this is not the sole bonding orbital and that there are many MOs of similar energy that have sigma character. This suggests that the view that aromaticity is defined by solely by orthogonal p<sub>z</sub> orbitals is flawed and that the real picture is far more complex. An example is included below, in which the MO has sigma character, but still represents a bonding orbital in which the electrons are delocalised (the nodes are atom-based and the MO is cyclic). This MO is formed from p-orbitals in the plane of the ring showing an effect known as σ-aromaticity. Thus, clearly, MO theory has shown that the Huckel view of aromaticity is not complete.

<div id="Delocalised sigma">
[[File:MO14_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]

[REF: L. ZH; ''et al'', ''Sigma-aromaticity and sigma-antiaromaticity in saturated inorganic rings'', J Phys Chem, 2005, 109, 16, 3711-3716]

[REF: S. Hadlington, ''Elusive σ aromaticity captured'', Chemistry World, 2014]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T15:08:13Z

Pg1716: /* Aromaticity: to be or not to be */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

<div id="Delocalised pz">
[[File:P_delocalised_Gobbett.png|frameless|500px|centre]]
</div>

However, MO calculations show that this is not the sole bonding orbital and that there are many MOs of similar energy that have sigma character. This suggests that the view that aromaticity is defined by solely by orthogonal p<sub>z</sub> orbitals is flawed and that the real picture is far more complex. An example is included below, in which the MO has sigma character, but still represents a bonding orbital in which the electrons are delocalised (the nodes are atom-based and the MO is cyclic). This MO is formed from p-orbitals in the plane of the ring showing an effect known as σ-aromaticity. Thus, clearly, MO theory has shown that the Huckel view of aromaticity is not complete.

<div id="Delocalised sigma">
[[File:MO14_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]

[REF: L. ZH; ''et al'', ''Sigma-aromaticity and sigma-antiaromaticity in saturated inorganic rings'', J Phys Chem, 2005, 109, 16, 3711-3716]

[REF: S. Hadlington, ''Elusive σ aromaticity captured'', Chemistry World, 2014]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T15:07:50Z

Pg1716: /* Aromaticity: to be or not to be */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

<div id="Delocalised pz">
[[File:P_delocalised_Gobbett.png|frameless|500px|centre]]
</div>

However, MO calculations show that this is not the sole bonding orbital and that there are many MOs of similar energy that have sigma character. This suggests that the view that aromaticity is defined by solely by orthogonal p<sub>z</sub> orbitals is flawed and that the real picture is far more complex. An example is included below, in which the MO has sigma character, but still represents a bonding orbital in which the electrons are delocalised (the nodes are atom-based and the MO is cyclic). This MO is formed from p-orbitals in the plane of the ring showing an effect known as σ-aromaticity. Thus, clearly, MO theory has shown that the Huckel view of aromaticity is not complete.

<div id="Delocalised sigma">
[[File:MO14_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]
[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]
[REF: L. ZH; ''et al'', ''Sigma-aromaticity and sigma-antiaromaticity in saturated inorganic rings'', J Phys Chem, 2005, 109, 16, 3711-3716]
[REF: S. Hadlington, ''Elusive σ aromaticity captured'', Chemistry World, 2014]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T15:04:09Z

Pg1716: /* Aromaticity: to be or not to be */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

<div id="Delocalised pz">
[[File:P_delocalised_Gobbett.png|frameless|500px|centre]]
</div>

However, MO calculations show that this is not the sole bonding orbital and that there are many MOs of similar energy that have sigma character. This suggests that the view that aromaticity is defined by solely by orthogonal p<sub>z</sub> orbitals is flawed and that the real picture is far more complex. An example is included below, in which the MO has sigma character, but still represents a bonding orbital in which the electrons are delocalised (the nodes are atom-based and the MO is cyclic). This MO is formed from p-orbitals in the plane of the ring showing an effect known as σ-aromaticity. Thus, clearly, MO theory has shown that the Huckel view of aromaticity is not complete.

<div id="Delocalised sigma">
[[File:MO14_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T14:57:51Z

Pg1716: /* Aromaticity: to be or not to be */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

<div id="Delocalised pz">
[[File:P_delocalised_Gobbett.png|frameless|500px|centre]]
</div>

However, MO calculations show that this is not the sole bonding orbital and that there are many MOs of similar energy that have sigma character. An example is included below, in which the MO has sigma character, but still represents a bonding orbital in which the electrons are delocalised (the nodes are atom-based and the MO is cyclic). This suggests that the view that aromaticity is defined by solely by orthogonal p<sub>z</sub> orbitals is flawed and that the real picture is far more complex.

<div id="Delocalised sigma">
[[File:MO14_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

File:P delocalised Gobbett.png

2018-05-18T14:50:26Z

Pg1716:

All Hail The Return Of GaussView

2018-05-18T14:48:51Z

Pg1716: /* Aromaticity: to be or not to be */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic''. ''Anti-aromatic'' compounds suffer from reduced stability, conversely to their ''aromatic'' equivalents (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which lowers their overall energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. For many of these compounds, MO theory backs up the conclusions of aromaticity. For example, computing MOs for benzene show the delocalised ring of electrons (from the p<sub>z</sub> orbitals of each C atom) above and below the plane of the ring:

[REF: M. Palusiak; T. Krygowski, ''Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings'', Chemistry Eur, 2007, 13, 7996-8006]

[REF: A. Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T14:34:13Z

Pg1716: /* Project: Aromaticity */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazine ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazine, NBO)
! scope="col" style="width: 250px;" | Borazine
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazine molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazine share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazine molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazine, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazine has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazine and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazine'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazine. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazine example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazine. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazine equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazine MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazine's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazine (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazine MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazine has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazine equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazine MO I
! scope="col" style="width: 333px;" | Borazine MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compound to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic'' (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which will almost certainly lower their energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. However, there is an increasing number of molecules for which the rules don't appear to matter; they display aromaticity without complying with Huckel!

[REF: A.Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T14:30:31Z

Pg1716: /* Borazene */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazine ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following borazine molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazine">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Borazine</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazene's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazene (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazene MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazene has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO I
! scope="col" style="width: 333px;" | Borazene MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compund to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic'' (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which will almost certainly lower their energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. However, there is an increasing number of molecules for which the rules don't appear to matter; they display aromaticity without complying with Huckel!

[REF: A.Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T14:27:02Z

Pg1716: /* Aromaticity: to be or not to be */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazene's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazene (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazene MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazene has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO I
! scope="col" style="width: 333px;" | Borazene MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability, lower reactivity and even bond lengths.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules, which attempted to explain aromaticity via a quantum mechanical approach:

For a compund to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

If a compound complied with these rules, it was said to be ''aromatic'' and if not is would be ''anti-aromatic'' (although typically compounds that are ''"anti-aromatic"'' tend to twist their conformations so that they are ''"non-aromatic"'' - this means they are no longer planar which will almost certainly lower their energy).

For many compounds, these rules work very well to describe and predict aromatic behavior. However, there is an increasing number of molecules for which the rules don't appear to matter; they display aromaticity without complying with Huckel!

[REF: A.Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T14:17:37Z

Pg1716: /* Aromaticity: to be or not to be */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazene's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazene (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazene MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazene has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO I
! scope="col" style="width: 333px;" | Borazene MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

Aromaticity is commonly thought of as a description of structures that have a similar set of characteristics caused by their electronic structure. The key characteristics are being planar and having a higher thermodynamic stability than expected due to a specific resonance between certain bonds. Other characteristics include relative chemical stability and lower reactivity.

The unique resonance was first suggested by Kekule in the 19<sup>th</sup> century and was greatly expanded on by Huckel in the 1930s. This lead to the development of Huckel's Rules:

For a compund to be aromatic, it must be:

- planar

- cyclic

- a continuous ring of p atomic orbitals perpendicular to plane of the ring

- have (4n + 2) π electrons in the conjugated system

[REF: A.Spivey, ''Aromatic Chemistry'', Imperial College, 2016-2017]

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T14:02:38Z

Pg1716: /* Aromatic Theory */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazene's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazene (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazene MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazene has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO I
! scope="col" style="width: 333px;" | Borazene MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromaticity: to be or not to be ====

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==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T13:57:53Z

Pg1716: /* Interesting MOs */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazene's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazene (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazene MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazene has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a symmetrical, bonding MO19, reflecting its higher degree of symmetry. In comparison, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO I
! scope="col" style="width: 333px;" | Borazene MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T13:56:54Z

Pg1716: /* Interesting MOs */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazene's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazene (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazene MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazene has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in symmetry. Benzene has a fairly symmetrical MO19 in this region, reflecting its higher degree of symmetry. In comparison, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (-0.31995 a.u.) and have a very similar shape. The differences arise from the differing electronegativities of both B and N, resulting in different distributions in the MOs. It would be an interesting extension to match these calculated MOs to their LCAO equivalents to better explain the results. Unfortunately, there was not sufficient time to do so.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Interesting MOs'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO I
! scope="col" style="width: 333px;" | Borazene MO II
|-
| <div id="MO19 Benzene">
[[File:Ofinterest_MO19_Benzene2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO18 Borazine">
[[File:Ofinterest_MO18_Borazene_a2_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO19 Borazine">
[[File:Ofinterest_MO18_Borazene_b2_Gobbett.png|frameless|333px|centre]]
</div>
|}

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

File:Ofinterest MO18 Borazene b2 Gobbett.png

2018-05-18T13:53:33Z

Pg1716:

File:Ofinterest MO18 Borazene b2.png

2018-05-18T13:52:52Z

Pg1716:

File:Ofinterest MO18 Borazene a2 Gobbett.png

2018-05-18T13:52:13Z

Pg1716:

File:Ofinterest MO19 Benzene2 Gobbett.png

2018-05-18T13:51:33Z

Pg1716:

All Hail The Return Of GaussView

2018-05-18T13:48:27Z

Pg1716: /* Interesting MOs */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazene's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazene (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazene MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazene has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from differences in electronegativity. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T13:44:45Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. The N p-orbitals are deeper in energy as N is more electronegative. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N means its p-orbital is deeper in energy and so dominates the character of the interaction. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaive and so its s-orbital is deeper in energy. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
''The lobes on the inside of the ring of borazene's MO16 are due to rounding errors in the generation of the MO''
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| These are the HOMO MOs for both benzene and borazene (MO20/21). They are each one of two degenerate orbitals and show '''pi''' bonding character. For each, the degenerate MO looks the same, but is simply rotated by 90<sup>o</sup>. In the case of benzene, the MOs are of higher symmetry. This is again due to the fact that each C contributes equally to the MO. Similarly, it is again the case that for the borazene MO, the contributions are not equal (N orbitals being deeper in energy) and so the distribution is not equal. This results in lower symmetry again, with more of the MO centred over the N atoms. Thus borazene has a higher energy HOMO.
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from atom subsitiution. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-18T13:33:08Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N constrains the size of the resulting lobe. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaivity and so its s-orbital dominates more. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
|-
| <div id="MO20 Benzene">
[[File:MO20_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO20 Borazene">
[[File:MO20_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| xxxx
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from atom subsitiution. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

File:MO20 Borazene Gobbett.png

2018-05-18T13:32:43Z

Pg1716:

File:MO20 Benzene Gobbett.png

2018-05-18T13:31:58Z

Pg1716:

All Hail The Return Of GaussView

2018-05-18T13:30:27Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| Shown here is MO13 of benzene and MO16 of borazene. In both cases, the MO shows bonding between a ring atom and its respective hydrogen atom. In each, this results in a '''sigma''' arrangement. In the case of benzene, the MO is composed of s-orbitals of the hydrogens and p-orbitals of the carbon atoms. The orbitals have alternating phases, suggesting non-bonding character (even perhaps slight anti-bonding character).
The borazene equivalent MO is composed of s-orbitals of the hydrogens and p-orbitals of either a boron or nitrogen atom. In this case, the relative size of each lobe is affected by the electronegativities of the atoms involved. Where an H s-orbital is interacting with an N p-orbital, the greater electronegativity of the N constrains the size of the resulting lobe. In the case of the H s-orbital is interacting with a B p-orbital, it is the H that is the more electronegaivity and so its s-orbital dominates more. Again, the orbitals have alternating phases, suggesting non-bonding to anti-bonding character.
It is due to the significantly reduced symmetry of the borazene MO that the energy difference between these two is more significant than the set above; the benzene MO is notably more symmetrical thus deeper in energy (more stable).
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|333px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|333px|centre]]
</div>
|| xxxx
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from atom subsitiution. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

File:MO15 Borazene Gobbett.png

2018-05-18T13:08:48Z

Pg1716:

All Hail The Return Of GaussView

2018-05-18T13:08:39Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

''include a pi MO''

''include a sigma MO''

''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by shape''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO15 Borazine">
[[File:MO15_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. Shown is MO14 for benzene and MO15 for borazene. For both molecules, the MO is composed of the p-orbitals of the ring atoms in the plane of ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry and slightly deeper in energy. This is because all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43197 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="MO13 Benzene">
[[File:AMO13_Benzene_Gobbett.png|frameless|333px|centre]]
</div>
|| <div id="MO16 Borazene">
[[File:AMO16_Borazene_Gobbett.png|frameless|333px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|333px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|333px|centre]]
</div>
|| xxxx
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from atom subsitiution. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

File:AMO16 Borazene Gobbett.png

2018-05-18T13:06:29Z

Pg1716:

File:AMO13 Benzene Gobbett.png

2018-05-18T13:05:50Z

Pg1716:

All Hail The Return Of GaussView

2018-05-18T12:55:20Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has an associative value of -135 kJmol<sup>-1</sup>. Hence, the dissociative bond energy is 135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene. It is worth noting that despite their different charge distributions, the two structures both have neutral overall charge.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

''include a pi MO''

''include a sigma MO''

''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by shape''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="MO14 Benzene">
[[File:MO14_Benzene_Gobbett.png|frameless|250px|centre]]
</div>
|| <div id="MO14 Borazine">
[[File:MO14_Borazene_Gobbett.png|frameless|250px|centre]]
</div>
|| This set of MOs shows a high energy '''sigma''' arrangement. MO14 for both molecules is composed of the p-orbitals of the atoms in the ring. The MO for benzene (E=-0.43854 a.u.) is higher in symmetry, as all the p-orbitals are equally contributing to the MO; whereas in the borazene example (E=-0.43399 a.u.) the symmetry is slightly lower due to the discrepancy between the B and N p-orbital contribution. However, the difference is less significant than in other MOs: both MOs in this case are similar in both shape and energy.
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from atom subsitiution. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

File:MO14 Borazene Gobbett.png

2018-05-18T12:47:12Z

Pg1716:

File:MO14 Benzene Gobbett.png

2018-05-18T12:46:18Z

Pg1716:

All Hail The Return Of GaussView

2018-05-18T12:43:28Z

Pg1716: /* Charge Comparison of Benzene and Borazene */

All Hail The Return Of GaussView

2018-05-18T12:40:29Z

Pg1716: /* Energy Calculations */

All Hail The Return Of GaussView

2018-05-17T20:35:56Z

Pg1716: /* BH3 */

All Hail The Return Of GaussView

2018-05-17T20:33:01Z

Pg1716: /* BH3 */

=== Introduction ===
A few choice words

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

<center><jmol>
<jmolApplet>
<title>BH3</title><color>white</color>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
</jmolApplet>
<jmolMenu>
<item><text>Start spinning</text><script>spin on</script></item>
<item><text>Stop spinning</text><script>spin off</script></item>
<menuHeight>-1</menuHeight>
</jmolMenu>
<jmolButton>
<script>console</script>
<text>open a console window</text>
</jmolButton>
</jmol></center>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has a value of -135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol></center>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

''include a pi MO''

''include a sigma MO''

''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by shape''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from atom subsitiution. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-17T20:30:22Z

Pg1716:

All Hail The Return Of GaussView

2018-05-17T20:29:24Z

Pg1716: /* BH3 */

All Hail The Return Of GaussView

2018-05-17T20:26:31Z

Pg1716:

All Hail The Return Of GaussView

2018-05-17T20:25:13Z

Pg1716: /* Borazene */

=== Introduction ===
A few choice words

=== Useful Base Wiki Code ===

<div id="Transition State Distance">
[[File:Question2HHHGOBBETT.png|frameless|500px|centre]]
</div>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! p<sub>1</sub> !! p<sub>2</sub> !! Energy (Kcal/mol) !! Plot !! Info
|-
| XXXXXX || XXXXXX || XXXXXX || XXXXXX || XXXXXX
|}

[[File:Vib1gobbetttester.ogv|thumb|500px|centre |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

[[File:A11v 1094228.ogv |thumb |200px |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has a value of -135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<center><jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

''include a pi MO''

''include a sigma MO''

''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by shape''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from atom subsitiution. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-17T20:17:48Z

Pg1716: /* Aromatic Theory */

=== Introduction ===
A few choice words

=== Useful Base Wiki Code ===

<div id="Transition State Distance">
[[File:Question2HHHGOBBETT.png|frameless|500px|centre]]
</div>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! p<sub>1</sub> !! p<sub>2</sub> !! Energy (Kcal/mol) !! Plot !! Info
|-
| XXXXXX || XXXXXX || XXXXXX || XXXXXX || XXXXXX
|}

[[File:Vib1gobbetttester.ogv|thumb|500px|centre |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

[[File:A11v 1094228.ogv |thumb |200px |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has a value of -135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

''include a pi MO''

''include a sigma MO''

''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by shape''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|}

==== Interesting MOs ====

The following MOs are found near the HOMO region of both molecules and serve to show the interesting disparity in shapes that arise from atom subsitiution. Benzene has a fairly symmetrical MO in this region, reflecting its higher degree of symmetry. In comparrsion, the shape of the borazene equivalent shows set of two degenerate non-bonding orbitals of very low symmetry (although it is clear they are degenerate as they have the same energy (xxx) and have ''a very similar shape'' -'''check'''.

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-17T20:01:30Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

=== Useful Base Wiki Code ===

<div id="Transition State Distance">
[[File:Question2HHHGOBBETT.png|frameless|500px|centre]]
</div>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! p<sub>1</sub> !! p<sub>2</sub> !! Energy (Kcal/mol) !! Plot !! Info
|-
| XXXXXX || XXXXXX || XXXXXX || XXXXXX || XXXXXX
|}

[[File:Vib1gobbetttester.ogv|thumb|500px|centre |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

[[File:A11v 1094228.ogv |thumb |200px |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has a value of -135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs

''include a pi MO''

''include a sigma MO''

''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by shape''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|}

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-17T20:00:40Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

=== Useful Base Wiki Code ===

<div id="Transition State Distance">
[[File:Question2HHHGOBBETT.png|frameless|500px|centre]]
</div>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! p<sub>1</sub> !! p<sub>2</sub> !! Energy (Kcal/mol) !! Plot !! Info
|-
| XXXXXX || XXXXXX || XXXXXX || XXXXXX || XXXXXX
|}

[[File:Vib1gobbetttester.ogv|thumb|500px|centre |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

[[File:A11v 1094228.ogv |thumb |200px |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has a value of -135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs
''include a pi MO''
''include a sigma MO''
''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by symmetry''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|}

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-17T20:00:22Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

=== Useful Base Wiki Code ===

<div id="Transition State Distance">
[[File:Question2HHHGOBBETT.png|frameless|500px|centre]]
</div>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! p<sub>1</sub> !! p<sub>2</sub> !! Energy (Kcal/mol) !! Plot !! Info
|-
| XXXXXX || XXXXXX || XXXXXX || XXXXXX || XXXXXX
|}

[[File:Vib1gobbetttester.ogv|thumb|500px|centre |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

[[File:A11v 1094228.ogv |thumb |200px |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has a value of -135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs
''include a pi MO''
''include a sigma MO''
''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by symmetry''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx

|}

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-17T19:59:58Z

Pg1716: /* Comparission of MOs */

=== Introduction ===
A few choice words

=== Useful Base Wiki Code ===

<div id="Transition State Distance">
[[File:Question2HHHGOBBETT.png|frameless|500px|centre]]
</div>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! p<sub>1</sub> !! p<sub>2</sub> !! Energy (Kcal/mol) !! Plot !! Info
|-
| XXXXXX || XXXXXX || XXXXXX || XXXXXX || XXXXXX
|}

[[File:Vib1gobbetttester.ogv|thumb|500px|centre |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

[[File:A11v 1094228.ogv |thumb |200px |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has a value of -135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BBr3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene.
|}

==== Comparission of MOs====

The MOs were calculated for both benzene and borazene and the top 26 were visualised. Below are the comparisons of three of those MOs
''include a pi MO''
''include a sigma MO''
''include an MO for which the energies / MO number does not match, even though it is the corresponding MO by symmetry''

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 333px;" | Benzene MO
! scope="col" style="width: 333px;" | Borazene MO
! scope="col" style="width: 333px;" | Analysis
|-
| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>|| <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| xxxx
|-
| xxxx || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|-
| xxxx || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|}

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

All Hail The Return Of GaussView

2018-05-17T19:14:06Z

Pg1716: /* Fini */

=== Introduction ===
A few choice words

=== Useful Base Wiki Code ===

<div id="Transition State Distance">
[[File:Question2HHHGOBBETT.png|frameless|500px|centre]]
</div>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! p<sub>1</sub> !! p<sub>2</sub> !! Energy (Kcal/mol) !! Plot !! Info
|-
| XXXXXX || XXXXXX || XXXXXX || XXXXXX || XXXXXX
|}

[[File:Vib1gobbetttester.ogv|thumb|500px|centre |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

[[File:A11v 1094228.ogv |thumb |200px |alt=A spacesuited astronaut slowly climbs down a ladder on a complicated metal structure, and then hops the last step onto a bright terrain. |Television clip of Buzz descending the ladder and stepping onto the moon. ]]

== EX<sub>3</sub> ==

==== BH<sub>3</sub> ====

''' B3LYP/6-31G level '''

The following BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency and vibrational analysis.

<div id="Summery First BH3">
[[File:SummeryinfogobbettV6.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

Click this [[Media:BH3 GOBBETT V5 FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BH3</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BH3 GOBBETT V5 FREQ.LOG</uploadedFileContents>
<script>frame 1.16</script>
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===== Vibrational Analysis =====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Table 1'''
! Frequency (cm<sup>1</sup>) !! Intensity (arbitrary units) !! Symmetry !! IR Active? !! Type
|-
| 1163 || 92 || A<sub>2</sub>" || Yes|| Out-of-Plane Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 1213 || 14 || E' || Very Slight || Bend
|-
| 2579 || 0 || A<sub>1</sub>' || No || Symmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|-
| 2712 || 126 || E' || Yes || Asymmetric Stretch
|}

<div id="BH3 IR Spec">
[[File:IRSPECgobbettV5.png|frameless|500px|centre]]
</div>

The IR spectrum shows three peaks, even though there are six vibrations. There are two reasons for this. Firstly, as the Symmetric Stretch (2579cm<sup>1</sup>) has no dipole moment, it does not show up on the IR spectrum as it is not IR active. Secondly, there are also two sets of degenerate vibrations: the Asymmetric Stretches (2712cm<sup>1</sup>) and the Bends (1213cm<sup>1</sup>). As they have the same frequency, their peaks overlap and appear as one.

===== MO Analysis =====

<div id="MO Diagram">
[[File:MOdiagramGobbett.png|frameless|500px|centre]]
</div>

[REF: Basis MO Diagram courtesy of P. Hunt, ''Lecture 4 Tutorial Problem Model Answers'', Can be accessed here: [http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf] (Accessed: 17/5/18)]

Here, the MO diagram clearly shows the difference between calculated MOs and LCAOs. Broadly speaking, the calculated MOs support the shape predicted by the LCAOs, but more effectively show the electron distribution and size of the orbitals. The calculated MOs also clearly show how higher MOs are increasingly diffuse; something that is not shown by the LCAO models.

==== NH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.5223 -11.4866 -0.0030 0.0246 0.1415 25.6160
Low frequencies --- 1089.6618 1694.1735 1694.1738
</pre>

Click this [[Media:NH3_GOBBETT_V1.LOG | <u>link</u>]] for the full .log file

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<title>NH3</title>
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<uploadedFileContents>NH3_GOBBETT_V1.LOG</uploadedFileContents>
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==== NH<sub>3</sub>BH<sub>3</sub> ====

''' B3LYP/6-31G (d,p) '''

The following NH<sub>3</sub>BH<sub>3</sub> molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_NH3BH3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.000523 0.001800 YES
RMS Displacement 0.000287 0.001200 YES

</pre>
<pre>
Low frequencies --- -0.0614 -0.0463 -0.0066 21.3815 21.3876 40.8513
Low frequencies --- 266.0674 632.3620 640.1229
</pre>

Click this [[Media:NH3BH3_GOBBETT_V4.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>NH3BH3</title>
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<color>white</color>
<size>500</size>
<uploadedFileContents>NH3BH3_GOBBETT_V4.LOG</uploadedFileContents>
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==== Energy Calculations ====

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Total Energies (a.u.)'''
! E(BH<sub>3</sub>) !! E(NH<sub>3</sub>) !! E(NH<sub>3</sub>BH<sub>3</sub>)
|-
| -26.61532342 || -56.55776863 || -83.22469013
|-
|}

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22469013 - [(-56.55776863) + (-26.61532342)]
= -0.05159808 a.u.

''The method of calculation we use is accurate to approx. 5 kJmol<sup>-1</sup>, but due to systematic errors we assume it is acceptable to report comparative values to the nearest 1 kJmol<sup>-1,</sup>. This translates as 0.00038 a.u.''

= -0.05160 a.u.
= -135 kJmol<sup>-1</sup>

Thus, the dative bond energy for the BH<sub>3</sub>-NH<sub>3</sub> molecule has a value of -135 kJmol<sup>-1</sup>. This makes it a comparatively weak bond {REF: C-C = 348 kJmol<sup>-1</sup>, H-H = 436 kJmol<sup>-1</sup>}.

[REF: University of Waterloo, ''Bond Lengths and Energies'', Link: [http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html] (Accessed: 17/5/18)]

==== BBr<sub>3</sub> ====

''' B3LYP/GEN '''

BBr<sub>3</sub> contains three heavy atoms (Br). To calculate their effect properly, we require the use of a pseudo-potential.

The following BBr<sub>3</sub> molecule was optimised via the Imperial cx1 HPC cluster. The optimisation was then checked by frequency analysis, again via the Imperial cx1 HPC cluster..

<div id="Summery First NH3">
[[File:SummeryinfogobbettV2_BBr3.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000018 0.001200 YES

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

Click this [[Media:BBr3_GOBBETT_output_3_freq4.log | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>BBr3</title>
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<size>500</size>
<uploadedFileContents>BBr3_GOBBETT_output_3_freq4.log</uploadedFileContents>
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{{DOI|10042/202430}}

== Project: Aromaticity ==

==== Benzene ====

''' B3LYP/6-31G (d,p)'''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery First NH3">
[[File:SummeryinfogobbettV1 Benzene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000193 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000787 0.001800 YES
RMS Displacement 0.000368 0.001200 YES

</pre>
<pre>
Low frequencies --- -11.6728 -0.0009 -0.0009 0.0001 6.6686 15.6846
Low frequencies --- 414.0392 414.6031 621.0860
</pre>

Click this [[Media:BENZENE_GOBBETT_V1_FREQ2.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BENZENE_GOBBETT_V1_FREQ2.LOG</uploadedFileContents>
<script>frame 1.16</script>
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==== Borazene ====

''' B3LYP/6-31G (d,p) LANL2DZ '''

The following benzene molecule was optimised. The optimisation was then checked by frequency analysis.

<div id="Summery Borazene">
[[File:SummeryinfogobbettV1_Borazene.png|frameless|500px|centre]]
</div>

<pre>

Item Value Threshold Converged?
Maximum Force 0.000197 0.000450 YES
RMS Force 0.000067 0.000300 YES
Maximum Displacement 0.000407 0.001800 YES
RMS Displacement 0.000163 0.001200 YES

</pre>
<pre>
Low frequencies --- -17.7329 -11.8586 -9.4862 -0.0008 -0.0002 0.0009
Low frequencies --- 288.9839 289.5006 404.2292
</pre>

Click this [[Media:BORAZENE_GOBBETT_V1_FREQ.LOG | <u>link</u>]] for the full .log file

<jmol><jmolApplet>
<title>Benzene</title>
<align>center</align>
<color>white</color>
<size>500</size>
<uploadedFileContents>BORAZENE_GOBBETT_V1_FREQ.LOG</uploadedFileContents>
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==== Charge Comparison of Benzene and Borazene ====

NBO charge analysis was undertaken for both structures. The colour range for both molecules set from -1.102 to 1.102, to ensure the images were visually comparable.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; width: 100%;"
|+ '''Benzene vs. Borazene'''
! scope="col" style="width: 250px;" | Benzene
! scope="col" style="width: 250px;" | Charge Distribution (Benzene, NBO)
! scope="col" style="width: 250px;" | Charge Distribution (Borazene, NBO)
! scope="col" style="width: 250px;" | Borazene
|-
| As one would expect, the carbon atoms all have the same charge distribution, as do the hydrogen atoms. They are all respectively in the same environment, thus their charge distribution ought to be equal. The C atoms are slightly more negatively charged as C is more electronegative than H (2.55 compared to 2.20 {Pauling Scale, RSC}) but the difference is very small, hence the charge difference is small too. This is why the colouring is dark in the image: both C and H are close to the middle of the scale (seen below) || <div id="Charge Distribution Benzene">
[[File:Benzene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| <div id="Charge Distribution Borazene">
[[File:Borazene_Gobbett_Charges2.png|frameless|250px|centre]]
</div>
|| The charge distribution is more interesting for the Borazene molecule. The most negatively charged atom present is Nitrogen (-1.102) as expected because it is the most electronegative (3.04 {Pauling Scale, RSC}). Boron is in fact less electronegative than hydrogen (2.04 compared to 2.20 {Pauling Scale, RSC}), hence the relative negative numbers on the hydrogen atoms bonded to B (although the difference is so small, the value is a tiny -0.077)
|-
| colspan="4" | <div id="Charge Scale">
[[File:Charge_Scale_Gobbett_2018.png|frameless|350px|centre]]
</div>
|-
| colspan="4" style="text-align: left| Thus it is clear that benzene and borazene share very different charge distributions. This is easy to see by eye, comparing the two images above. It is also simply explained by the Pauling scale of electronegativity. In benzene, as discussed, there is a high level of symmetry and the charge distribution is even across the molecule; a slightly electronegative centre surrounded by electropositive hydrogens. In stark contrast is the borazene molecule, in which the central ring is made up of two atoms with electronegativities above and below that of hydrogen. This also has an effect on bond length. In the benzene molecule, the C-H bond distances are all equal, as are all the C-C bond distances. In borazene, the B-N bond distances are equal due to the alternating structure of the ring, but the B-H / N-H bond distances are not the same, lowering the symmetry of the molecule. N holds the H atoms very strongly, as it is significantly more electronegative. This means it also draws electron density to itself, leaving the hydrogen with a slight positive charge. Boron, as discussed, is electropositive with regard to H and so the B-H bonds are much longer. Thus borazene has a much more varied, alternating charge structure to its isoelectric equivalent, benzene.
|}

==== Comparission of MOs====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Aromatic Theory ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included

==== Fini ====

The following MOs are the 120 levels for benzene and borazine respectively. They are included for their sheer aesthetic joy, not for their relevance to any interesting chemistry. To all intents and purposes, these MOs don't exist and can't be reproduced experimentally (to a certainty of over 99.9%), but they are really pretty.

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett.png|frameless|500px|centre]]
</div>

They look even funkier in the "mesh" setting:

<div id="Benzene120">
[[File:Pretty_Benzene_Gobbett2.png|frameless|500px|centre]]
</div>

<div id="Borazine120">
[[File:Pretty_Borazine_Gobbett2.png|frameless|500px|centre]]
</div>

File:Pretty Benzene Gobbett2.png

2018-05-17T19:12:42Z

Pg1716:

File:Pretty Borazine Gobbett2.png

2018-05-17T19:10:25Z

Pg1716: