ChemWiki - User contributions [en]

Rep:Mod:az916

2018-05-25T16:57:30Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2715
|126
|A1'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|370px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|350px|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px|center]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px|center]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>The molecule must be cyclic and planar</li>
<li>The molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px|center]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px|center]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across each carbon in the ring. Electron density is concentrated around the nitrogen atoms in borazine, resulting in lower resonance stability. Symmetry can be used to indicate aromatic stability. The benzene orbital has D6 symmetry whilst the borazine one has D3h symmetry. This lower symmetry aligns with lower resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px|center]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px|center]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs contain a node and are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px|center]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px|center]]
|}

The two MOs pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-25T16:52:53Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2715
|126
|A1'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|370px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|350px|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px|center]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px|center]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>The molecule must be cyclic and planar</li>
<li>The molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px|center]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px|center]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px|center]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px|center]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px|center]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px|center]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-25T16:46:22Z

Az916: /* Vibrational spectrum for BH3 */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|1213
|14
|E'
|very slight
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2715
|126
|A1'
|yes
|asymmetric stretch
|-
|2715
|126
|E'
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|370px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|350px|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px|center]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px|center]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px|center]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px|center]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px|center]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px|center]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px|center]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px|center]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:13:48Z

Az916: /* Charge Distribution Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|370px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|350px|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px|center]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px|center]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px|center]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px|center]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px|center]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px|center]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px|center]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px|center]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:10:02Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px|center]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px|center]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px|center]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px|center]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px|center]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px|center]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px|center]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px|center]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:09:21Z

Az916: /* Charge Distribution Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px|center]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px|center]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:09:03Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px|center]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px|center]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:08:37Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px]|center]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px]|center]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:08:15Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px|center]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px]|center]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px|center]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px]|center]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px|center]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px|center]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:07:36Z

Az916: /* Charge Distribution Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]|center]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:07:19Z

Az916: /* Charge Distribution Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px|center]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]|center]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:05:29Z

Az916: /* Charge Distribution Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref name ="electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref name = "electroneg">A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:02:54Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|320px]] ||
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|300px]]
|}

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|320px]] ||
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|300px]]
|}

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|320px]] ||
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|300px]]
|}

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:01:04Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|320px]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|320px]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|320px]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:00:40Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|300px]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|300px]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px]] ||
[[File:Ahz_borazine_orb18.PNG|thumb|Borazine MO 18|300px]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T18:00:10Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==
{| border="1" align="center"
|-
|[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|320px]] ||
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|300px]]
|}

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|320px]] ||
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|300px]]
|}

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

{| border="1" align="center"
|-
| [[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|320px]] ||
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|300px]]
|}

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T17:56:59Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene. This effect is often attributed to overlap of p orbitals, but literature indicates that it is sigma orbitals which predominantly delocalise, forcing pi electrons to then delocalise as symmetry is increased<ref>Influence of .sigma. and .pi. electrons on aromaticity
Karl Jug and Andreas M. Koester
Journal of the American Chemical Society 1990 112 (19), 6772-6777
DOI: 10.1021/ja00175a005</ref>. The sigma element of aromaticty is evident in these orbitals. Both consist of bonding s orbitals of one phase. The benzene orbital has higher symmetry than the borazine one, owing to an equal charge distribution across the molecule. Electron density is more evenly distributed in this orbital relative to borazine, resulting in higher resonance stability.

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

Both orbitals pictures also display delocalised sigma bonding frameworks. The MOs are likely to be less of a contributing factor to aromaticity than benzene and borazine orbital 7, since the MOs are not distributed over the entire molecule. Given that two sigma MOs in each molecule contribute to delocalisation relative to only one pi MO, it is likely that sigma bonding has a greater impact on delocalisation as previously stated in literature. The borazine MO in this case has distorted electron distribution with a higher density around nitrogen, likely resulting in less delocalisation and stability. The phase formed of p orbitals in the ring's plane pointing towards the center is likely to be the predominant factor in delocalisation. Since this ring is intact in borazine unlike the ring of s orbitals from hydrogen, the orbital will still contribute to delocalisation.

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

The two orbitals pictured feature pz orbitals perpendicular to the ring plane. These are typically associated with aromaticity, but are should not be considered in isolation. Electron density is again very symmetrically distributed in benzene, but distorted towards nitrogen in borazine. The distortion of all orbitals involved in aromaticity in borazine results in a lower degree of electron delocalisation and therefore lower resonance energy than benzene.

Rep:Mod:az916

2018-05-24T17:25:10Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

A characteristic feature of aromatic systems is an intermediate bond length relative to the equivalent alkene.

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

Rep:Mod:az916

2018-05-24T17:01:01Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
</ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

Sigma bonding MOs

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

Rep:Mod:az916

2018-05-24T17:00:49Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
<ol>

Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

Sigma bonding MOs

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

Rep:Mod:az916

2018-05-24T16:58:29Z

Az916: /* Aromaticity Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

Aromaticity is typically defined using Hückel's rules:
<ol>
<li>Molecule must be cyclic and planar</li>
<li>Molecule must have 4n+2 π electrons</li>
<li>The π orbitals must be contiguous in the ring</li>
<ol>
Whilst this definition is adequate in many cases, a molecular orbital approach reveals greater insight than this qualitative definition. Aromaticity as a general concept imparts stability to cyclic molecules through resonance. This can be applied to molecules that are not planar, and extends beyond π orbitals exclusively <ref>M. B. Smith, J. March, Marchs Advances Organic Chemistry, 5th Edition, Wiley, New York, 2001, p. 48</ref>. σ MOs can also be delocalised, imparting stability by diffusing electron density. Both of these factors must be considered in discussing the extent of aromaticity.

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

Sigma bonding MOs

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

Rep:Mod:az916

2018-05-24T16:33:42Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent to the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. The benzene one is slightly anti-bonding in character abd both have 3 nodes. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms to the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

Rep:Mod:az916

2018-05-24T16:27:35Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. Both are slightly anti-bonding in character, with 3 nodes in each case. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms than the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma slightly anti-bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

Rep:Mod:az916

2018-05-24T16:26:39Z

Az916: /* Charge Distribution Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|320px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. Both are slightly anti-bonding in character, with 3 nodes in each case. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms than the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

Rep:Mod:az916

2018-05-24T16:26:11Z

Az916: /* Charge Distribution Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|350px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. Both are slightly anti-bonding in character, with 3 nodes in each case. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms than the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

Rep:Mod:az916

2018-05-24T16:24:01Z

Az916: /* Orbital Comparison */

=Day 1=
==BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_bh3_summary.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000049 0.001800 YES
RMS Displacement 0.000032 0.001200 YES
Predicted change in Energy=-8.985249D-10
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BH3_FREQ.LOG| 6-31G(d.p) BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.6235 -0.3404 -0.0053 14.5386 17.7840 17.7950
Low frequencies --- 1163.0535 1213.2211 1213.2238
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A1
|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
|A1
|yes
|asymmetric stretch
|-
|2715
|126
|E
|no
|asymmetric stretch
|}

[[File:Ahz_bh3_spectrum.JPG|500px]]

BH3 has 6 calculated modes of vibration. However, in the spectrum above, only 3 peaks are observed. At 1213 cm-1 and 2715-1 there are in fact two pairs of degenerate vibration modes. Since the vibrations have the same energy, they occur at the same wavenumber (E=hc/λ). Stretching is higher in energy relative to bond deformation, resulting in the stretching peak occuring at a much higher frequency. The vibration at 2582 does not produce any signal in the spectrum as it is totally symmetric. A change in dipole is required to absorb IR radiation and produce a peak, thus a totally symmetric vibration will not result in radiation absorption.

===Molecular orbitals of BH3===
[[File:Ahz_bh3mo.PNG|thumb|MO diagram<ref>Hunt Research Group tutorial problem sheet, URL: http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, Accessed: 22/05/2018</ref> of BH3 featuring 'real' orbitals and LCAOs|500px|center]]

Both LCAO and 'real' MO approaches produce orbitals of the same symmetry and phases. The LCAO molecular orbitals are qualitatively determined by combining orbitals of similar energy and particular symmetries. The real MOs are likely to combine more atomic orbitals than LCAO predicts. Since electron-electron repulsion is also considered, it more predicts the distribution of electron density. MOs are therefore more spread out over the entire molecule.

Qualitative MO theory is likely adequate for predicting the general shapes and phases of orbitals in simple systems, but a computational approach is much more accurate for more complicated ones.

==NH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3sumtab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000092 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000305 0.001800 YES
RMS Displacement 0.000102 0.001200 YES
Predicted change in Energy=-1.875177D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3OPT2FREQ.LOG | 6-31G(d.p) NH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3OPT2FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==NH3BH3==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahznh3bh3sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000181 0.001200 YES
Predicted change in Energy=-1.139042D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZNH3BH3FREQ.LOG | 6-31G(d.p) NH3BH3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -32.4235 -32.4224 -11.4276 -0.0044 0.0115 0.0476
Low frequencies --- 1088.7628 1694.0251 1694.0251
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZNH3BH3FREQ.LOG </uploadedFileContents>
</jmolApplet></jmol>

===Bond strength and energy discussion===

The energy of the N-B bond in ammonia borane can be calculated by subracting the total energy of ammonia and borane from the energy of NH3BH3:
<ul>
<li>E(NH3)= -56.55776871 a.u </li>
<li>E(BH3)= -26.61532364 a.u. </li>
<li>E(NH3BH3)= -83.22468887 a.u. </li>
<li>ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = (-83.22468887)-[(-56.55776871)+(-26.61532364)] = -0.05159652 a.u.≈ 135 KJ.mol-1</li>
</ul>

The bond energy obtained of 135 KJ.mol-1 aligns well with the literature value of ~130 KJ.mol-1<ref>Moury, R.; Demirci, U.B. Hydrazine Borane and Hydrazinidoboranes as Chemical Hydrogen Storage Materials. Energies 2015, 8, 3118-3141</ref>

The dative bond is of medium strength. An ordinary covalent bond such as N-H has a dissociation enthalphy of 386 KJ.mol<ref>Wired Chemist, URL: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html, Accessed: 22/05/2018</ref>. It is still much larger than weak dipole interactions such as hydrogen bonds at around 2-5 KJ.mol-1<ref>Porter, T., Heim, G., & Kubiak, C. (2017). Effects of electron transfer on the stability of hydrogen bonds. Chemical Science., 8(11), 7324-7329.</ref>.

==BBr3==
Computation method: B3LYP/6-31G(d,p)LANL2DZ

===Completed frequency file D-Space link===
http://hdl.handle.net/10042/202445

===Summary table===
[[File:Ahz_bbr3_sum.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000015 0.000300 YES
Maximum Displacement 0.000122 0.001800 YES
RMS Displacement 0.000069 0.001200 YES
Predicted change in Energy=-3.491783D-09
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:Ahz_bbr3_freq_server_optimised.log| 6-31G(d.p) BBr3 frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -4.0153 -0.0002 0.0000 0.0001 1.7448 3.4070
Low frequencies --- 155.8881 155.9561 267.7048
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Ahz_bbr3_freq_server_optimised.log</uploadedFileContents>
</jmolApplet></jmol>

=Project: Aromaticity=

==Benzene==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_benzene_sum_table.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000097 0.001800 YES
RMS Displacement 0.000036 0.001200 YES
Predicted change in Energy=-1.579511D-08
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BENZENE_OPT_FREQ.LOG | 6-31G(d.p) benzene frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -0.0088 -0.0041 -0.0041 12.5838 12.5838 16.4940
Low frequencies --- 414.3526 414.3526 621.2606
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>benzene</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BENZENE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Borazine==
Computation method: RB3LYP/6-31G(d.p)

===Summary table===
[[File:Ahz_borazine_sum_tab.PNG|300px]]

===Item table===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000111 0.000450 YES
RMS Force 0.000046 0.000300 YES
Maximum Displacement 0.000380 0.001800 YES
RMS Displacement 0.000097 0.001200 YES
Predicted change in Energy=-1.890893D-07
Optimization completed.
-- Stationary point found.
</pre>

===Frequency analysis log File===
[[Media:AHZ_BORAZINE_OPT_FREQ.LOG | 6-31G(d.p) borazine frequency log file]]

===Low Frequency Lines===
<pre>
Low frequencies --- -6.0214 -5.8056 -5.2959 -0.0106 0.0584 0.1775
Low frequencies --- 289.2503 289.2583 403.8913
</pre>

===jmol Image===
<jmol><jmolApplet>
<title>borazine</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>AHZ_BORAZINE_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

==Charge Distribution Comparison==

{| border="1" align="center"
|-
| [[File:Ahz_benzene_charge.PNG|thumb|Benzene charge distribution in colour range 1 to -1|300px]] ||
[[File:Ahz_borazine_charge.PNG|thumb|Borazine charge distribution in colour range 1 to -1|300px]]
|}

In benzene, carbon is slightly more electronegative than hydrogen (2.55 vs 2.20<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), thus carbon holds more negative charge than hydrogen. The charge on carbon is -0.239, whilst hydrogen has a charge of 0.239. Due to the symmetry of benzene, there is no overall dipole, however. There must be an asymmetric charge distribution over the length of a molecule to cause a net dipole moment. Any vector drawn from a negatively charged to positively charged area of the molecule is cancelled by an opposing vector mirrored through the inversion center.

Borazine on the other hand has a significantly different charge distribution. Nitrogen is significantly more electronegative than boron (3.04 vs 2.04<ref>A.L. Allred, J. Inorg. Nucl. Chem., 1961, 17, 215</ref>), and a large charge disparity results. The hydrogens bonded to boron are very slightly negative (-0.077) whilst those bonded to nitrogen are relatively positive (0.432). Unlike benzene, borazine does not have a center of inversion. As a result, the molecule possesses a net dipole moment. Each boron is opposing a nitrogen in the ring, so a vector from negative to positive charge can be drawn accross the molecule.

==Orbital Comparison==

[[File:Ahz_benzene_orb21.PNG|thumb|Benzene MO 21|center]]
[[File:Ahz_borazine_orb21.PNG|thumb|Borazine MO 21|center]]

Both orbitals consist of two sets of pi systems separated by a nodal plane. In benzene, the MO still has an ungerade center of inversion as the shapes of the pi systems are identical on both sides of the molecule. In borazine, however, there is distortion of the orbitals due to a net dipole in the molecule. Nitrogen's electronegativity withdraws electron density in this predominantly bonding orbital. The upper system contains 2 nitrogen atoms which reduce the orbital size around boron. This is espeically pronounced in the lower system, where the orbital boundary surface does not completely cover the two boron atoms adjacent the nitrogen.

[[File:Ahz_benzene_orb16.PNG|thumb|Benzene MO 16|center]]
[[File:Ahz_borazine_orb13.PNG|thumb|Borazine MO 13|center]]

Two comparable sigma bonding molecular orbitals are pictured above. Both are slightly anti-bonding in character, with 3 nodes in each case. Despite consisting of equivalent atomic orbitals, the benzene MO is very dissimilar to the borazine one. In benzene, the MO has an ungerade center of inversion as electron density distribution in the upper and lower systems is the same. In borazine, the nitrogen in the lower system skews the atomic p orbitals in the plane of the ring so that there are no longer any nodes through bonds in the molecule. The ordering of this MO in borazine is 13, whilst in benzene it is 16. Part of the reason for this significant difference in energy ordering may be due to this lack of nodal plane through bonds. Repulsion between atoms could be slightly reduced, rendering this MO more stable in relative terms than the benzene counterpart.

[[File:Ahz_benzene_orb19.PNG|thumb|Benzene MO 19|center]]
[[File:Ahz_borazine_orb18.PNG|Borazine MO 18|center]]

These comparable sigma bonding MOs exhibit significant differences in lobe size due to dipole moment disparaties. There are 4 nodal planes in both MOs, and the benzene MO is gerade with respect to inversion. Benzene has no dipole moment, so the s lobes on the two hydrogens at the top and bottom of the molecule are of equal size. In contrast, the hydrogen lobe bonded to boron is much larger than that bonded to nitrogen. As identified int the charge distribution analysis, this N-H hydrogen is slightly positive whilst the B-H one is slightly negative. This causes the large disparity in lobe size. The Hydrogens bonded to the borons adjacent to the lower nitrogen also have a large degree of electron density relative to the comparable ones on benzene.

==Aromaticity Comparison==

[[File:Ahz_benzene_orb7.PNG|thumb|Benzene MO 7|center]]
[[File:Ahz_borazine_orb7.PNG|thumb|Borazine MO 7|center]]

[[File:Ahz_benzene_orb12.PNG|thumb|Benzene MO 12|center]]
[[File:Ahz_borazine_orb10.PNG|thumb|Borazine MO 10|center]]

[[File:Ahz_benzene_orb17.PNG|thumb|Benzene MO 17|center]]
[[File:Ahz_borazine_orb17.PNG|thumb|Borazine MO 17|center]]

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Az916: Az916 uploaded a new version of File:Ahz borazine charge.PNG

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Az916: