== BH3 ==
=== 3-21G Optimisation Summary ===

[[File:GP_bh3_opt_image.png|250px]]

==== Summary Table ====

<pre> Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000759 0.001800 YES
RMS Displacement 0.000442 0.001200 YES

</pre>

=== 6-31G Optimisation Summary ===

[[File:GP_bh3_opt_image_accurate.png|250px]]

==== Summary Table ====

<pre> Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

BH3 belongs to the D3h point group but due to the limitations of the Gaussian software it has been assigned as CS. D3h symmetry was imposed on the optimised molecule before carrying out a frequency analysis.

=== Frequency Analysis ===

Link to BH3 frequency analysis log file:[[Media:GP_BH3_FREQ_ACCURATE.LOG|here]]

<pre>
Low frequencies --- -0.4059 -0.1955 -0.0054 25.3480 27.3326 27.3356
Low frequencies --- 1163.1913 1213.3139 1213.3166
</pre>

<jmol><jmolApplet>
<title>BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GP_BH3_FREQ_ACCURATE.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== BH3 Vibrations ====
{| class="wikitable"
!Wavenumber (cm-1)
!Intensity (arbitrary units)
!Symmetry
!IR active?
!Type
|-
|1163
|93
|A2<nowiki>''</nowiki>
|yes
|out-of-plane bend
|-
|1213
|14
|E
|very slight
|bend
|-
|1213
|14
|E
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|yes
|asymmetric stretch
|}

==== BH3 IR Spectrum ====

[[File:GP_IR_SPECTRUM_BH3.PNG]]

Fewer than 6 peaks in the IR spectrum even though there are 6 vibrations as some of the vibrations will not be accompanied by a change in dipole moment (a requirement in order to be IR active).

==== BH3 MO Diagram ====

[[File:GP_bh3_MOS.PNG]]

In general, the MOs almost mirror the LCAOs. The a1' MO shows that the MO is diffuse over the entire molecule as opposed to the more atom localised image presented by LCAO. The e' LCAO derived from the px AO suggests that this MO should be equal in bonding and antibonding character. However, the MO shows that this is not the case with one side being more diffuse than the other. Overall, the similarity between the LCAO diagrams and the real MOs suggest that qualitative MO theory is more than accurate enough for our purposes here.

== NH3 ==

=== 6-31G Optimisation Summary ===
[[File:GP_NH3_OPT_IMAGE.PNG]]
==== Summary Table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000100 0.000450 YES
RMS Force 0.000050 0.000300 YES
Maximum Displacement 0.000177 0.001800 YES
RMS Displacement 0.000113 0.001200 YES
</pre>

NH3 belongs to the C3V point group but due to the limitations of the Gaussian software it has been assigned as CS. C3V symmetry was imposed on the optimised molecule before carrying out a frequency analysis.

Link to NH3 frequency analysis log file:[[Media:GP_NH3_OPT_C3V.LOG|here]]

<pre>
Low frequencies --- -33.1843 -32.6528 -32.6527 -0.0012 -0.0012 0.0024
Low frequencies --- 1088.9832 1693.8057 1693.8057

</pre>

<jmol><jmolApplet>
<title>NH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GP_NH3_OPT_C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 ==

=== 6-31G Optimisation Summary ===
[[File:GP_nh3bh3_opt_image.PNG]]
==== Summary Table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>
Link to NH3BH3 frequency analysis log file:[[Media:GP_NH3BH3_OPT_FREQ.LOG ‎|here]]

<pre>
Low frequencies --- -0.0012 -0.0011 0.0011 17.1488 17.8526 37.4337
Low frequencies --- 265.8896 632.2187 639.3610
</pre>

<jmol><jmolApplet>
<title>NH3BH3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GP_NH3BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(BH3)= -26.61532350

E(NH3)= -56.55776870

E(NH3BH3)= -83.22468893

Dissociation Energy = 0.05159673 au

Dissociation Energy = 135 kJ/mol

Thus it is a relatively weak bond, lower in energy than that of comparable single bonds shown in the table below. <ref name="Bond Strength" />

{| class="wikitable" border="1"
|+ Bond Dissociation Energies
! Bond !! Energy (kJ/mol)
|-
| B-N || 135
|-
| O-O || 146
|-
| N-N || 160
|-
| C-C || 347

|}

== BBr3 ==

=== Optimisation Summary ===
[[File:GP_BBr3_OPT_IMAGE.PNG]]
==== Summary Table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
</pre>

BBr3 belongs to the D3h point group but due to the limitations of the Gaussian software it has been assigned as CS. D3h symmetry was imposed on the optimised molecule before carrying out a frequency analysis.

Link to BBr3 frequency analysis log file:[[Media:GP_BBR3_OPT_FREQ.LOG‎|here]]

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

<jmol><jmolApplet>
<title>BBr3 molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GP_BBR3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

{{DOI|10042/202466}}

== Benzene ==

=== Optimisation Summary ===
[[File:GP_BENZENE_OPT_IMAGE.PNG ‎]]
==== Summary Table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000082 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000305 0.001200 YES
</pre>

Benzene belongs to the D6h point group but due to the limitations of the Gaussian software it has been assigned as C1. D6h symmetry was imposed on the optimised molecule before carrying out a frequency analysis.

Link to benzene frequency analysis log file:[[Media:GP_BENZENE_OPT_FREQUENCY.LOG‎|here]]

<pre>
Low frequencies --- -13.7810 -12.9763 -11.9029 -0.0002 0.0001 0.0009
Low frequencies --- 414.0699 414.1914 620.9703
</pre>

<jmol><jmolApplet>
<title>Benzene molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GP_BENZENE_OPT_FREQUENCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

=== Optimisation Summary ===
[[File:GP_BORAZINE_OPT_IMAGE.PNG]]
==== Summary Table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000276 0.001800 YES
RMS Displacement 0.000077 0.001200 YES
</pre>

Borazine belongs to the D3h point group but due to the limitations of the Gaussian software it has been assigned as C1. D3h symmetry was imposed on the optimised molecule before carrying out a frequency analysis.

Link to borazine frequency analysis log file:[[Media:‎GP_BORAZINE_OPT_FREQ.LOG|here]]

<pre>
Low frequencies --- -7.5576 -0.0008 -0.0002 0.0008 7.2648 13.2011
Low frequencies --- 288.5679 290.5561 404.2330
</pre>

<jmol><jmolApplet>
<title>Borazine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GP_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine:Benzene Charge Analysis ==

{| class="wikitable" border="1"
|+
! Borazine !! Benzene
|-
| [[File:GP_BORAZINE_CHARGE.PNG]] || [[File:GP_BENZENE_CHARGE.PNG]]
|}

=== Formal Charges ===

{| class="wikitable" border="1"
|+
! Benzene !! Formal Charge (NPH)
|-
| C || -0.239
|-
| H || 0.239
|}

{| class="wikitable" border="1"
|+
! Borazine !! Formal Charge (NPH)
|-
| B || 0.747
|-
| N || -1.102
|-
| H (B-H) || -0.077
|-
| H (N-H) || 0.432
|}

Benzene is D6h symmetric and shows just two charge environments. All 6 carbon atoms are equivalent and hence carry the same charge and the same is seen for the 6 hydrogen atoms which are in identical environments so carry the same charge. The electronegativity of carbon is 2.55 whilst that of hydrogen is 2.20.<ref name="Electronegativity">https://www.angelo.edu/faculty/kboudrea/periodic/trends_electronegativity.htm</ref> As carbon is the more electronegativte atom, it draws electron density within the C-H bond towards itself resulting in the negative charge whilst the hydrogen carries a positive charge.

With borazine, charge is distributed unevenly between the boron and nitrogen atoms. Nitrogen is more electronegative than Boron (3.04 compared to 2.04 respectively) and hence carries the negative charge.<ref name="Electronegativity">https://www.angelo.edu/faculty/kboudrea/periodic/trends_electronegativity.htm</ref> Another consequence of the difference in electronegativities is the B-H hydrogens being slightly negative in charge whilst the N-H hydrogens are positive. As nitrogen is significantly more electronegative than hydrogen it draws the electron density away from the hydrogen atom. Whereas hydrogen and boron have very similar electronegativities resulting in only very small charge values across the B-H bonds. Boron is slightly less electronegative than hydrogen and thus the B-H hydrogens are the only ones to carry a negative charge in these two examples.

=== Comparing MOs ===

{| class="wikitable" border="1"
|+
! Borazine !! Benzene !! Discussion
|-
| [[File:BORAZINE_MO21.PNG]] MO21 || [[File:BENZENE_MO21.PNG]] MO21 || Both MOS are pi-bonding with mostly p-atomic orbital contributions. While the benzene MO is symmetric (E1g), the borazine MO is not. Again this is due to distortions in electron density as a result of the differing energies of the boron and nitrogen atoms. As nitrogen is lower in energy and this is a bonding MO, we expect a greater contribution to the MO from the nitrogen orbitals.
|-
| [[File:BORAZINE_MO19.PNG]] MO19 || [[File:BENZENE_MO19.PNG]] MO19 || Here, the benzene sigma antibonding MO is symmetric due to the equivalency of the carbon atoms. This is not the case for the borazine antibonding sigma MO; boron is higher in energy than nitrogen and so has a greater contribution to the antibonding MO. Hence this MO is distorted towards the boron atom. When considering atomic orbital contributions, we can see the hydrogen s-orbital contributions at the top and bottom of each MO and carbon p-orbitals dominating in the central region. [[File:BENZENE_AO.PNG]]
|-
| [[File:BORAZINE_MO15.PNG]] MO15 || [[File:BENZENE_MO14.PNG]] MO14 || The high energy sigma bonding MOs for borazine and benzene are very similar. There is a subtle difference between the two, while the orbitals in the benzene MO are completley symmetric, those of borazine differ slightly due to the different electronic contributions from the boron and nitrogen atoms to the MO. The high symmetry of the benzene MO is reflective of its D6h point group.
|}

== Aromaticity ==
The concept of aromaticity is used to describe the unusual stability of molecules with alternating double bonds such as benzene. To be aromatic the molecule must: be planar, cyclic, have a contiguous ring of p-orbitals and contain 4n+2 pi-electrons. This final rule derives from Huckel theory. Aromaticity can be illustrated using MO theory by taking a simple example, benzene. Rather than show localised areas of electron density, the MO is delocalised across the whole molecule. Simply, this could be thought of as the overalp of neighbouring pz orbitals resulting in delocalisation.

However, this simple picture breaks down when considering larger molecules with fused rings such as pyrene.<ref name="Pyrene">Roberts, John D.; Streitwieser, Andrew, Jr.; Regan, Clare M. (1952). "Small-Ring Compounds. X. Molecular Orbital Calculations of Properties of Some Small-Ring Hydrocarbons and Free Radicals". J. Am. Chem. Soc. 74 (18): 4579–82. doi:10.1021/ja01138a038 </ref> Whilst containing 4n pi electrons, it is still an aromatic molecule, breaking the Huckel rule of aromaticity. Aromatic compounds need not be planar; for example pyrenophane is not planar yet still aromatic.<ref name="Pyrenophane">Boazhong Zhang, Gregory P.Manning, (2008).Nonplanar Aromatic Compounds. 9. Synthesis, Structure, and Aromaticity of 1:2,13:14-Dibenzo[2]paracyclo[2](2,7)- pyrenophane-1,13-diene".Org. Lett., 10 (2), pp 273–276 DOI: 10.1021/ol702703b </ref>. Thus a more sophisticated model is required.This is an active area of research and a consensus has not yet been reached. It has been postulated that the sigma structure is a greater contributor to aromaticity than previously suspected. <ref name="Rules of aromaticity">Palusiak, M. and Krygowski, T. (2007), Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and
Quasi-Aromatic Rings. Chemistry - A European Journal, 13:7996-8006. doi:10.1002/chem.200700250</ref>

== References ==

<references>
<ref name="Bond Strength">http://butane.chem.uiuc.edu/cyerkes/Chem104ACSpring2009/Genchemref/bondenergies.html</ref>
</references>

2018-05-25T11:50:45Z

2018-05-24T17:40:24Z

Gp316: