File:HARICHAUHANSIGMA.PNG

2018-05-25T16:42:42Z

Hc2616:

HariChauhanInorganic

2018-05-25T16:42:26Z

Hc2616: /* Aromaticity */

== BH3 ==

=== B3LYP/6-31G Level ===
[[File:HariChauhan BH3Optimization 6-21G..PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

[[Media:HARICHAUHAN_BH3OPTIMIZATION_6-21G_FREQ.log|BH3_frequency.log]]

<pre> Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHAN_BH3OPTIMIZATION_6-21G_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'
|slightly
|bend
|-
|1213
|14
|E'
|slightly
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:HariChauhanBH3Spectrum.png|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Only three peaks appear in the predicted spectrum because there are two pairs of E' vibrational modes that are degenerate, hence they appear as one signal each. Furthermore, the A1' symmetric stretch does not produce a change in the dipole moment of the molecule so is not IR active.

[[File:HariChauhanBH3MO2.png|thumb|none|MO diagram for BH3 adapted from provided tutorial sheet|left]]

The a1' molecular orbital looks different from that predicted by LCAO. The s orbitals on the hydrogen atoms appear much larger in the calculated MO. This suggests that the LCAO approach to predicting molecular orbitals may have some inaccuracies.

== NH3 ==

=== B3LYP/6-31G Level ===

[[File:HariChauhanNH3Summary.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES</pre>

[[Media:HariChauhanHN3.log|NH3_frequency.log]]

<pre> Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHANNH3.log</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1089
|145
|A
|yes
|asymmetric strech
|-
|1693
|14
|E
|slightly
|bend
|-
|1693
|14
|E
|slightly
|bend
|-
|3461
|1
|A1'
|very slightly
|symmetric stretch
|-
|3589
|0
|E
|no
|asymmetric stretch
|-
|3589
|0
|E
|no
|asymmetric stretch
|}

[[File:HARICHAUHANNH3SPECTRUM.LOG|500px|none]]

Similar to BH3, NH3 has two sets of degenerate vibrational modes. However one of these pairs is IR inactive. Therefore, only three signals are predicted in the IR spectrum.

== BH3NH3 ==

=== B3LYP/6-31G Level ===

[[File:HARICHAUHANBH3NH3SUMMARY.PNG|400px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000350 0.000450 YES
RMS Force 0.000112 0.000300 YES
Maximum Displacement 0.001350 0.001800 YES
RMS Displacement 0.000450 0.001200 YES</pre>

[[Media:HARICHAUHANBH3NH3_OPT.LOG|NH3BH3_frequency.log]]

<pre> Low frequencies --- -0.0262 -0.0082 -0.0023 9.6688 9.6769 37.9651
Low frequencies --- 265.3241 634.4274 639.1700</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHANBH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3NH3====
Due to the large number of vibrational modes in BH3NH3, a screenshot of the vibrations predicted by Gaussian is provided. A total of 11 bands should be observed, although some with very low intensity. Also, some are very close in energy so may overlap.

[[File:HARICHAUHANBH3NH3VIBRATIONS.PNG|none|400px]]
[[File:HARICHAUHANBH3NH3SPECTRUM.PNG|none|400px]]

====Calculating B-N Bond Energy in BH3NH3====

<pre>E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - (-56.55777 - 26.61532) = -0.05167 a.u.

-0.05167 a.u. * 2625 = -136 kJmol-1</pre>

The energy of the B-N bond in BH3NH3 is -136 kJmol-1

Comparing this bond with the C-C bond strength in ethane, which is isoelectronic, the B-N bond is significantly weaker. In ethane, the C-C bond is around 364 kJmol-1, over double that of the B-N bond strength. This is likely due to the large electronegativity difference between B and N.

== BBr3 ==

=== B3LYP/6-31G(d,p)LANL2DZ Level ===
[[File:HARICHAUHANBBR3SUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
</pre>

[[Media:HARICHAUHAN_BBR3OPTIMIZATION.LOG|BBr3_frequency.log]]

<pre> Low frequencies --- -0.0135 -0.0064 -0.0046 2.4669 2.4670 4.8600
Low frequencies --- 155.9626 155.9646 267.7022</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHAN_BBR3OPTIMIZATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BBr3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|156
|0
|E'
|no
|bend
|-
|156
|0
|E'
|no
|bend
|-
|268
|0
|A1'
|no
|symmetric stretch
|-
|378
|4
|A2"
|slightly
|out-of-plane bend
|-
|763
|320
|E'
|yes
|asymmetric stretch
|-
|763
|320
|E'
|yes
|asymmetric stretch
|}

[[File:HariChauhanBBr3Spectrum.png|none|500px|An IR Spectrum of BBr3 Predicted by Gaussian]]

Only one peak is seen in this spectrum as the two stretches at 763 cm-1 have far higher intensity than the other IR active stretch at 378 cm-1.

{{DOI|10042/202470}}

== Benzene ==

=== B3LYP/6-31G Level ===
[[File:HARICHAUHANBENZENESUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000084 0.000300 YES
Maximum Displacement 0.000767 0.001800 YES
RMS Displacement 0.000328 0.001200 YES</pre>

[[Media:HARICHAUHANBENZENE.LOG|Benzene_frequency.log]]

<pre> Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0054 -0.0054 0.0004
Low frequencies --- 414.1239 414.1239 620.9400</pre>

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

====Vibrational spectrum for Benzene====
[[File:HARICHAUHANBENZENEVIBRATIONS.PNG|500px]]

[[File:HARICHAUHANBENZENESPECTRUM.PNG|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Although benzene clearly has very many vibrational modes, due to its high symmetry, only a few are IR active. This explains why only 4 peaks are observed in its IR spectrum.

== Borazine ==

=== B3LYP/6-31G Level ===
[[File:HARICHAUHANBORAZINESUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000443 0.000450 YES
RMS Force 0.000179 0.000300 YES
Maximum Displacement 0.000882 0.001800 YES
RMS Displacement 0.000400 0.001200 YES</pre>

[[Media:HARICHAUHANBORAZINE.LOG|Borazine_frequency.log]]

<pre> Low frequencies --- -0.0045 -0.0033 -0.0031 5.3417 5.3626 5.9709
Low frequencies --- 289.8780 289.8786 404.4105</pre>

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

====Vibrational spectrum for Borazine====
[[File:HARICHAUHANBORAZINEVIBRATIONS.PNG|300px]]

[[File:HARICHAUHANBORAZINESPECTRUM.PNG|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Borazine has the same number of vibrational modes as benzene, however, due to its lower symmetry, more of these are IR active, which is why it shows 6 active signals in the IR spectrum.

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

{| class="wikitable"
|+
|-
|Benzene || Borazine
|-
|[[File:HARICHAUHANBENZENECHARGE.PNG|300px]]
|[[File:HARICHAUHANBORAZINECHARGE.PNG|300px]]
|-
|}

The brighter colours imply a higher magnitude of charge, with red implying a negative charge and green implying a positive charge.

Because carbon and hydrogen have very close electronegativities, the C-H bond has a large amount of covalent character. The C-C bond, being homonuclear, is completely covalent. Therefore, there is little separation of charge in benzene. Because carbon is a little more electronegative than hydrogen, a negative charge of -0.239 resides on the carbon atoms, with +0.239 on the hydrogen atoms. However, due to the D6h point group of the molecule, the sum of the C-H bond dipoles is zero, giving the benzene molecule an overall zero dipole moment.

In borazine, there is a higher separation of charge, shown by the brighter colours in the figure above. Nitrogen has a significantly higher electronegativity than boron and hydrogen, making the N-B and N-H bonds have a large dipole moment. Comparing the B-H and N-H bonds, the hydrogen atoms bonded to boron show little charge but the hydrogen atoms bonded to nitrogen have a charge of +0.432 as electrons in the N-H bond are drawn closer to the nitrogen.

In borazine, a large amount of negative charge resides on the Nitrogen atoms, with the boron and hydrogen atoms having positive charge, however due to the D3h point group of the molecule, the dipole moments of these polar bonds sums to zero, to give borazine no overall dipole moment.

Both molecules have a total charge of zero, so summing up the total charge gives zero in both cases.

===Comparison of Molecular Orbitals===

{| class="wikitable"
|+
|-
|Benzene || Borazine ||Comparison
|-
|style="width: 200pt;" |[[File:HARICHAUHANBENZENEMO12.PNG|300px]]
|style="width: 200pt;" |[[File:HARICHAUHANBORAZINEMO10.PNG|300px]]
|style="width: 500pt;" |MO 12 in benzene and 10 in borazine. Both of these MOs have a large amount of bonding character resulting from overlap of orbitals in the center of the ring in the plane of the molecule. They both result from in-phase overlap of the 1s orbital on hydrogen with the carbon 2p-orbitals along the C-H bonds. In borazine, the 1s on the carbon atoms bonded to boron don't contribute to this MO. This is likely because these hydrogen atoms are roughly neutral, so the 1s electrons are too high in energy to contribute.
|-
|[[File:HARICHAUHANBENZENEMO17.PNG|300px]]
|[[File:HARICHAUHANBORAZINEMO17.PNG|300px]]
|style="width: 500pt;" | MO17 in benzene and borazine. In both benzene and borazine this MO has a large amount of bonding character with a nodal plane in the plane of the molecule. It results from the in phase overlap of the 2p-orbitals adjacent to the ring. In benzene, each carbon contributes equally to this MO giving the MO a C6 rotational axis. In borazine however, there is a slightly larger contribution from the p-orbitals on nitrogen than on boron. This is because the 2p on nitrogen is lower in energy so contributes more to this bonding orbital. This gives this MO a C3 rotational axis.
|-
|[[File:HARICHAUHANBENZENEMO23.PNG|300px]]
|[[File:HARICHAUHANBORAZINEMO23.PNG|300px]]
|style="width: 500pt;" | MO23 in benzene and borazine. These MOs are overall antibonding and result in the out of phase overlap of four p-orbitals perpendicular to the ring. In benzene, each of these 2p-orbitals contributes equally as they are equivalent. In borazine however, the two 2p-orbitals on boron contribute a larger amount than the two 2p-orbitals on nitrogen. This is because this MO is anti-bonding and the 2p on boron are higher in energy than on nitrogen, so are closer in energy to this MO.
|-
|}

== Aromaticity ==

Hückel proposed a few criteria which a molecule must meet in order to be considered aromatic. It must be cyclic, planar, have a continuous system of p-orbitals adjacent to the ring and contain 4n+2 π-electrons in this π-system. This approach to aromaticity suggests that the aromatic stabilization of benzene comes largely from the molecular orbital shown above with an area of electron density above and below the ring of the molecule (MO 17).

However, it is now well known that planarity is not a requirement for aromaticity. At 20K, it has been shown that benzene, in a crystal structure, adopts a chair conformation.<ref>DOI: 10.1002/chem.200700250</ref> This shows a flaw in Huckel's theory and suggests that there is much more to aromaticity that he originally suggested. In fact, aromaticity is a word used to describe a number of stabilizing effects with the planar π-system being only one of these.

Sigma aromaticity, for example, is displayed in the MO shown. This is caused by the in-phase overlap of p-orbitals in the plane of the ring that face along the B-N bonds. This allows electrons in these p-orbitals to also delocalise over the aromatic molecule. [[File:HARICHAUHANBORAZINESIGMA.png|right|400px]] Sigma aromaticity also exists in molecules that don't resemble anything suggested by Huckel. For example, stabilization due to aromaticity and destabilization due to anti-aromaticity has been shown to exist in inroganic cages. [[File:HARICHAUHANSIGMA.PNG|thumb|Non-planar molecules that display sigma-aromaticity and anti-aromaticity]]<ref>DOI: 10.1021/jp048541o</ref>.

HariChauhanInorganic

2018-05-25T16:41:48Z

Hc2616: /* Aromaticity */

== BH3 ==

=== B3LYP/6-31G Level ===
[[File:HariChauhan BH3Optimization 6-21G..PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

[[Media:HARICHAUHAN_BH3OPTIMIZATION_6-21G_FREQ.log|BH3_frequency.log]]

<pre> Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHAN_BH3OPTIMIZATION_6-21G_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'
|slightly
|bend
|-
|1213
|14
|E'
|slightly
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:HariChauhanBH3Spectrum.png|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Only three peaks appear in the predicted spectrum because there are two pairs of E' vibrational modes that are degenerate, hence they appear as one signal each. Furthermore, the A1' symmetric stretch does not produce a change in the dipole moment of the molecule so is not IR active.

[[File:HariChauhanBH3MO2.png|thumb|none|MO diagram for BH3 adapted from provided tutorial sheet|left]]

The a1' molecular orbital looks different from that predicted by LCAO. The s orbitals on the hydrogen atoms appear much larger in the calculated MO. This suggests that the LCAO approach to predicting molecular orbitals may have some inaccuracies.

== NH3 ==

=== B3LYP/6-31G Level ===

[[File:HariChauhanNH3Summary.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES</pre>

[[Media:HariChauhanHN3.log|NH3_frequency.log]]

<pre> Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHANNH3.log</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1089
|145
|A
|yes
|asymmetric strech
|-
|1693
|14
|E
|slightly
|bend
|-
|1693
|14
|E
|slightly
|bend
|-
|3461
|1
|A1'
|very slightly
|symmetric stretch
|-
|3589
|0
|E
|no
|asymmetric stretch
|-
|3589
|0
|E
|no
|asymmetric stretch
|}

[[File:HARICHAUHANNH3SPECTRUM.LOG|500px|none]]

Similar to BH3, NH3 has two sets of degenerate vibrational modes. However one of these pairs is IR inactive. Therefore, only three signals are predicted in the IR spectrum.

== BH3NH3 ==

=== B3LYP/6-31G Level ===

[[File:HARICHAUHANBH3NH3SUMMARY.PNG|400px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000350 0.000450 YES
RMS Force 0.000112 0.000300 YES
Maximum Displacement 0.001350 0.001800 YES
RMS Displacement 0.000450 0.001200 YES</pre>

[[Media:HARICHAUHANBH3NH3_OPT.LOG|NH3BH3_frequency.log]]

<pre> Low frequencies --- -0.0262 -0.0082 -0.0023 9.6688 9.6769 37.9651
Low frequencies --- 265.3241 634.4274 639.1700</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHANBH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3NH3====
Due to the large number of vibrational modes in BH3NH3, a screenshot of the vibrations predicted by Gaussian is provided. A total of 11 bands should be observed, although some with very low intensity. Also, some are very close in energy so may overlap.

[[File:HARICHAUHANBH3NH3VIBRATIONS.PNG|none|400px]]
[[File:HARICHAUHANBH3NH3SPECTRUM.PNG|none|400px]]

====Calculating B-N Bond Energy in BH3NH3====

<pre>E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - (-56.55777 - 26.61532) = -0.05167 a.u.

-0.05167 a.u. * 2625 = -136 kJmol-1</pre>

The energy of the B-N bond in BH3NH3 is -136 kJmol-1

Comparing this bond with the C-C bond strength in ethane, which is isoelectronic, the B-N bond is significantly weaker. In ethane, the C-C bond is around 364 kJmol-1, over double that of the B-N bond strength. This is likely due to the large electronegativity difference between B and N.

== BBr3 ==

=== B3LYP/6-31G(d,p)LANL2DZ Level ===
[[File:HARICHAUHANBBR3SUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
</pre>

[[Media:HARICHAUHAN_BBR3OPTIMIZATION.LOG|BBr3_frequency.log]]

<pre> Low frequencies --- -0.0135 -0.0064 -0.0046 2.4669 2.4670 4.8600
Low frequencies --- 155.9626 155.9646 267.7022</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHAN_BBR3OPTIMIZATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BBr3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|156
|0
|E'
|no
|bend
|-
|156
|0
|E'
|no
|bend
|-
|268
|0
|A1'
|no
|symmetric stretch
|-
|378
|4
|A2"
|slightly
|out-of-plane bend
|-
|763
|320
|E'
|yes
|asymmetric stretch
|-
|763
|320
|E'
|yes
|asymmetric stretch
|}

[[File:HariChauhanBBr3Spectrum.png|none|500px|An IR Spectrum of BBr3 Predicted by Gaussian]]

Only one peak is seen in this spectrum as the two stretches at 763 cm-1 have far higher intensity than the other IR active stretch at 378 cm-1.

{{DOI|10042/202470}}

== Benzene ==

=== B3LYP/6-31G Level ===
[[File:HARICHAUHANBENZENESUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000084 0.000300 YES
Maximum Displacement 0.000767 0.001800 YES
RMS Displacement 0.000328 0.001200 YES</pre>

[[Media:HARICHAUHANBENZENE.LOG|Benzene_frequency.log]]

<pre> Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0054 -0.0054 0.0004
Low frequencies --- 414.1239 414.1239 620.9400</pre>

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

====Vibrational spectrum for Benzene====
[[File:HARICHAUHANBENZENEVIBRATIONS.PNG|500px]]

[[File:HARICHAUHANBENZENESPECTRUM.PNG|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Although benzene clearly has very many vibrational modes, due to its high symmetry, only a few are IR active. This explains why only 4 peaks are observed in its IR spectrum.

== Borazine ==

=== B3LYP/6-31G Level ===
[[File:HARICHAUHANBORAZINESUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000443 0.000450 YES
RMS Force 0.000179 0.000300 YES
Maximum Displacement 0.000882 0.001800 YES
RMS Displacement 0.000400 0.001200 YES</pre>

[[Media:HARICHAUHANBORAZINE.LOG|Borazine_frequency.log]]

<pre> Low frequencies --- -0.0045 -0.0033 -0.0031 5.3417 5.3626 5.9709
Low frequencies --- 289.8780 289.8786 404.4105</pre>

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

====Vibrational spectrum for Borazine====
[[File:HARICHAUHANBORAZINEVIBRATIONS.PNG|300px]]

[[File:HARICHAUHANBORAZINESPECTRUM.PNG|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Borazine has the same number of vibrational modes as benzene, however, due to its lower symmetry, more of these are IR active, which is why it shows 6 active signals in the IR spectrum.

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

{| class="wikitable"
|+
|-
|Benzene || Borazine
|-
|[[File:HARICHAUHANBENZENECHARGE.PNG|300px]]
|[[File:HARICHAUHANBORAZINECHARGE.PNG|300px]]
|-
|}

The brighter colours imply a higher magnitude of charge, with red implying a negative charge and green implying a positive charge.

Because carbon and hydrogen have very close electronegativities, the C-H bond has a large amount of covalent character. The C-C bond, being homonuclear, is completely covalent. Therefore, there is little separation of charge in benzene. Because carbon is a little more electronegative than hydrogen, a negative charge of -0.239 resides on the carbon atoms, with +0.239 on the hydrogen atoms. However, due to the D6h point group of the molecule, the sum of the C-H bond dipoles is zero, giving the benzene molecule an overall zero dipole moment.

In borazine, there is a higher separation of charge, shown by the brighter colours in the figure above. Nitrogen has a significantly higher electronegativity than boron and hydrogen, making the N-B and N-H bonds have a large dipole moment. Comparing the B-H and N-H bonds, the hydrogen atoms bonded to boron show little charge but the hydrogen atoms bonded to nitrogen have a charge of +0.432 as electrons in the N-H bond are drawn closer to the nitrogen.

In borazine, a large amount of negative charge resides on the Nitrogen atoms, with the boron and hydrogen atoms having positive charge, however due to the D3h point group of the molecule, the dipole moments of these polar bonds sums to zero, to give borazine no overall dipole moment.

Both molecules have a total charge of zero, so summing up the total charge gives zero in both cases.

===Comparison of Molecular Orbitals===

{| class="wikitable"
|+
|-
|Benzene || Borazine ||Comparison
|-
|style="width: 200pt;" |[[File:HARICHAUHANBENZENEMO12.PNG|300px]]
|style="width: 200pt;" |[[File:HARICHAUHANBORAZINEMO10.PNG|300px]]
|style="width: 500pt;" |MO 12 in benzene and 10 in borazine. Both of these MOs have a large amount of bonding character resulting from overlap of orbitals in the center of the ring in the plane of the molecule. They both result from in-phase overlap of the 1s orbital on hydrogen with the carbon 2p-orbitals along the C-H bonds. In borazine, the 1s on the carbon atoms bonded to boron don't contribute to this MO. This is likely because these hydrogen atoms are roughly neutral, so the 1s electrons are too high in energy to contribute.
|-
|[[File:HARICHAUHANBENZENEMO17.PNG|300px]]
|[[File:HARICHAUHANBORAZINEMO17.PNG|300px]]
|style="width: 500pt;" | MO17 in benzene and borazine. In both benzene and borazine this MO has a large amount of bonding character with a nodal plane in the plane of the molecule. It results from the in phase overlap of the 2p-orbitals adjacent to the ring. In benzene, each carbon contributes equally to this MO giving the MO a C6 rotational axis. In borazine however, there is a slightly larger contribution from the p-orbitals on nitrogen than on boron. This is because the 2p on nitrogen is lower in energy so contributes more to this bonding orbital. This gives this MO a C3 rotational axis.
|-
|[[File:HARICHAUHANBENZENEMO23.PNG|300px]]
|[[File:HARICHAUHANBORAZINEMO23.PNG|300px]]
|style="width: 500pt;" | MO23 in benzene and borazine. These MOs are overall antibonding and result in the out of phase overlap of four p-orbitals perpendicular to the ring. In benzene, each of these 2p-orbitals contributes equally as they are equivalent. In borazine however, the two 2p-orbitals on boron contribute a larger amount than the two 2p-orbitals on nitrogen. This is because this MO is anti-bonding and the 2p on boron are higher in energy than on nitrogen, so are closer in energy to this MO.
|-
|}

== Aromaticity ==

Hückel proposed a few criteria which a molecule must meet in order to be considered aromatic. It must be cyclic, planar, have a continuous system of p-orbitals adjacent to the ring and contain 4n+2 π-electrons in this π-system. This approach to aromaticity suggests that the aromatic stabilization of benzene comes largely from the molecular orbital shown above with an area of electron density above and below the ring of the molecule (MO 17).

However, it is now well known that planarity is not a requirement for aromaticity. At 20K, it has been shown that benzene, in a crystal structure, adopts a chair conformation.<ref>DOI: 10.1002/chem.200700250</ref> This shows a flaw in Huckel's theory and suggests that there is much more to aromaticity that he originally suggested. In fact, aromaticity is a word used to describe a number of stabilizing effects with the planar π-system being only one of these.

Sigma aromaticity, for example, is displayed in the MO shown. This is caused by the in-phase overlap of p-orbitals in the plane of the ring that face along the B-N bonds. This allows electrons in these p-orbitals to also delocalise over the aromatic molecule. [[File:HARICHAUHANBORAZINESIGMA.png|right|200px]] Sigma aromaticity also exists in molecules that don't resemble anything suggested by Huckel. For example, stabilization due to aromaticity and destabilization due to anti-aromaticity has been shown to exist in inroganic cages. [[File:HARICHAUHANSIGMA.PNG|thumb|Non-planar molecules that display sigma-aromaticity and anti-aromaticity<ref>DOI: 10.1021/jp048541o</ref>.

HariChauhanInorganic

2018-05-25T16:32:19Z

Hc2616: /* Aromaticity */

== BH3 ==

=== B3LYP/6-31G Level ===
[[File:HariChauhan BH3Optimization 6-21G..PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

[[Media:HARICHAUHAN_BH3OPTIMIZATION_6-21G_FREQ.log|BH3_frequency.log]]

<pre> Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHAN_BH3OPTIMIZATION_6-21G_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'
|slightly
|bend
|-
|1213
|14
|E'
|slightly
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:HariChauhanBH3Spectrum.png|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Only three peaks appear in the predicted spectrum because there are two pairs of E' vibrational modes that are degenerate, hence they appear as one signal each. Furthermore, the A1' symmetric stretch does not produce a change in the dipole moment of the molecule so is not IR active.

[[File:HariChauhanBH3MO2.png|thumb|none|MO diagram for BH3 adapted from provided tutorial sheet|left]]

The a1' molecular orbital looks different from that predicted by LCAO. The s orbitals on the hydrogen atoms appear much larger in the calculated MO. This suggests that the LCAO approach to predicting molecular orbitals may have some inaccuracies.

== NH3 ==

=== B3LYP/6-31G Level ===

[[File:HariChauhanNH3Summary.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES</pre>

[[Media:HariChauhanHN3.log|NH3_frequency.log]]

<pre> Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHANNH3.log</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1089
|145
|A
|yes
|asymmetric strech
|-
|1693
|14
|E
|slightly
|bend
|-
|1693
|14
|E
|slightly
|bend
|-
|3461
|1
|A1'
|very slightly
|symmetric stretch
|-
|3589
|0
|E
|no
|asymmetric stretch
|-
|3589
|0
|E
|no
|asymmetric stretch
|}

[[File:HARICHAUHANNH3SPECTRUM.LOG|500px|none]]

Similar to BH3, NH3 has two sets of degenerate vibrational modes. However one of these pairs is IR inactive. Therefore, only three signals are predicted in the IR spectrum.

== BH3NH3 ==

=== B3LYP/6-31G Level ===

[[File:HARICHAUHANBH3NH3SUMMARY.PNG|400px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000350 0.000450 YES
RMS Force 0.000112 0.000300 YES
Maximum Displacement 0.001350 0.001800 YES
RMS Displacement 0.000450 0.001200 YES</pre>

[[Media:HARICHAUHANBH3NH3_OPT.LOG|NH3BH3_frequency.log]]

<pre> Low frequencies --- -0.0262 -0.0082 -0.0023 9.6688 9.6769 37.9651
Low frequencies --- 265.3241 634.4274 639.1700</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHANBH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3NH3====
Due to the large number of vibrational modes in BH3NH3, a screenshot of the vibrations predicted by Gaussian is provided. A total of 11 bands should be observed, although some with very low intensity. Also, some are very close in energy so may overlap.

[[File:HARICHAUHANBH3NH3VIBRATIONS.PNG|none|400px]]
[[File:HARICHAUHANBH3NH3SPECTRUM.PNG|none|400px]]

====Calculating B-N Bond Energy in BH3NH3====

<pre>E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - (-56.55777 - 26.61532) = -0.05167 a.u.

-0.05167 a.u. * 2625 = -136 kJmol-1</pre>

The energy of the B-N bond in BH3NH3 is -136 kJmol-1

Comparing this bond with the C-C bond strength in ethane, which is isoelectronic, the B-N bond is significantly weaker. In ethane, the C-C bond is around 364 kJmol-1, over double that of the B-N bond strength. This is likely due to the large electronegativity difference between B and N.

== BBr3 ==

=== B3LYP/6-31G(d,p)LANL2DZ Level ===
[[File:HARICHAUHANBBR3SUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
</pre>

[[Media:HARICHAUHAN_BBR3OPTIMIZATION.LOG|BBr3_frequency.log]]

<pre> Low frequencies --- -0.0135 -0.0064 -0.0046 2.4669 2.4670 4.8600
Low frequencies --- 155.9626 155.9646 267.7022</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHAN_BBR3OPTIMIZATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BBr3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|156
|0
|E'
|no
|bend
|-
|156
|0
|E'
|no
|bend
|-
|268
|0
|A1'
|no
|symmetric stretch
|-
|378
|4
|A2"
|slightly
|out-of-plane bend
|-
|763
|320
|E'
|yes
|asymmetric stretch
|-
|763
|320
|E'
|yes
|asymmetric stretch
|}

[[File:HariChauhanBBr3Spectrum.png|none|500px|An IR Spectrum of BBr3 Predicted by Gaussian]]

Only one peak is seen in this spectrum as the two stretches at 763 cm-1 have far higher intensity than the other IR active stretch at 378 cm-1.

{{DOI|10042/202470}}

== Benzene ==

=== B3LYP/6-31G Level ===
[[File:HARICHAUHANBENZENESUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000084 0.000300 YES
Maximum Displacement 0.000767 0.001800 YES
RMS Displacement 0.000328 0.001200 YES</pre>

[[Media:HARICHAUHANBENZENE.LOG|Benzene_frequency.log]]

<pre> Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0054 -0.0054 0.0004
Low frequencies --- 414.1239 414.1239 620.9400</pre>

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

====Vibrational spectrum for Benzene====
[[File:HARICHAUHANBENZENEVIBRATIONS.PNG|500px]]

[[File:HARICHAUHANBENZENESPECTRUM.PNG|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Although benzene clearly has very many vibrational modes, due to its high symmetry, only a few are IR active. This explains why only 4 peaks are observed in its IR spectrum.

== Borazine ==

=== B3LYP/6-31G Level ===
[[File:HARICHAUHANBORAZINESUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000443 0.000450 YES
RMS Force 0.000179 0.000300 YES
Maximum Displacement 0.000882 0.001800 YES
RMS Displacement 0.000400 0.001200 YES</pre>

[[Media:HARICHAUHANBORAZINE.LOG|Borazine_frequency.log]]

<pre> Low frequencies --- -0.0045 -0.0033 -0.0031 5.3417 5.3626 5.9709
Low frequencies --- 289.8780 289.8786 404.4105</pre>

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

====Vibrational spectrum for Borazine====
[[File:HARICHAUHANBORAZINEVIBRATIONS.PNG|300px]]

[[File:HARICHAUHANBORAZINESPECTRUM.PNG|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Borazine has the same number of vibrational modes as benzene, however, due to its lower symmetry, more of these are IR active, which is why it shows 6 active signals in the IR spectrum.

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

{| class="wikitable"
|+
|-
|Benzene || Borazine
|-
|[[File:HARICHAUHANBENZENECHARGE.PNG|300px]]
|[[File:HARICHAUHANBORAZINECHARGE.PNG|300px]]
|-
|}

The brighter colours imply a higher magnitude of charge, with red implying a negative charge and green implying a positive charge.

Because carbon and hydrogen have very close electronegativities, the C-H bond has a large amount of covalent character. The C-C bond, being homonuclear, is completely covalent. Therefore, there is little separation of charge in benzene. Because carbon is a little more electronegative than hydrogen, a negative charge of -0.239 resides on the carbon atoms, with +0.239 on the hydrogen atoms. However, due to the D6h point group of the molecule, the sum of the C-H bond dipoles is zero, giving the benzene molecule an overall zero dipole moment.

In borazine, there is a higher separation of charge, shown by the brighter colours in the figure above. Nitrogen has a significantly higher electronegativity than boron and hydrogen, making the N-B and N-H bonds have a large dipole moment. Comparing the B-H and N-H bonds, the hydrogen atoms bonded to boron show little charge but the hydrogen atoms bonded to nitrogen have a charge of +0.432 as electrons in the N-H bond are drawn closer to the nitrogen.

In borazine, a large amount of negative charge resides on the Nitrogen atoms, with the boron and hydrogen atoms having positive charge, however due to the D3h point group of the molecule, the dipole moments of these polar bonds sums to zero, to give borazine no overall dipole moment.

Both molecules have a total charge of zero, so summing up the total charge gives zero in both cases.

===Comparison of Molecular Orbitals===

{| class="wikitable"
|+
|-
|Benzene || Borazine ||Comparison
|-
|style="width: 200pt;" |[[File:HARICHAUHANBENZENEMO12.PNG|300px]]
|style="width: 200pt;" |[[File:HARICHAUHANBORAZINEMO10.PNG|300px]]
|style="width: 500pt;" |MO 12 in benzene and 10 in borazine. Both of these MOs have a large amount of bonding character resulting from overlap of orbitals in the center of the ring in the plane of the molecule. They both result from in-phase overlap of the 1s orbital on hydrogen with the carbon 2p-orbitals along the C-H bonds. In borazine, the 1s on the carbon atoms bonded to boron don't contribute to this MO. This is likely because these hydrogen atoms are roughly neutral, so the 1s electrons are too high in energy to contribute.
|-
|[[File:HARICHAUHANBENZENEMO17.PNG|300px]]
|[[File:HARICHAUHANBORAZINEMO17.PNG|300px]]
|style="width: 500pt;" | MO17 in benzene and borazine. In both benzene and borazine this MO has a large amount of bonding character with a nodal plane in the plane of the molecule. It results from the in phase overlap of the 2p-orbitals adjacent to the ring. In benzene, each carbon contributes equally to this MO giving the MO a C6 rotational axis. In borazine however, there is a slightly larger contribution from the p-orbitals on nitrogen than on boron. This is because the 2p on nitrogen is lower in energy so contributes more to this bonding orbital. This gives this MO a C3 rotational axis.
|-
|[[File:HARICHAUHANBENZENEMO23.PNG|300px]]
|[[File:HARICHAUHANBORAZINEMO23.PNG|300px]]
|style="width: 500pt;" | MO23 in benzene and borazine. These MOs are overall antibonding and result in the out of phase overlap of four p-orbitals perpendicular to the ring. In benzene, each of these 2p-orbitals contributes equally as they are equivalent. In borazine however, the two 2p-orbitals on boron contribute a larger amount than the two 2p-orbitals on nitrogen. This is because this MO is anti-bonding and the 2p on boron are higher in energy than on nitrogen, so are closer in energy to this MO.
|-
|}

== Aromaticity ==

Hückel proposed a few criteria which a molecule must meet in order to be considered aromatic. It must be cyclic, planar, have a continuous system of p-orbitals adjacent to the ring and contain 4n+2 π-electrons in this π-system. This approach to aromaticity suggests that the aromatic stabilization of benzene comes largely from the molecular orbital shown above with an area of electron density above and below the ring of the molecule (MO 17).

However, it is now well known that planarity is not a requirement for aromaticity. At 20K, it has been shown that benzene, in a crystal structure, adopts a chair conformation.<ref>DOI: 10.1002/chem.200700250</ref> In fact, aromaticity is a word used to describe a number of stabilizing effects with the planar π-system being only one of these.

Sigma aromaticity, for example, is displayed in the MO shown. This is caused by the in-phase overlap of p-orbitals in the plane of the ring that face along the B-N bonds. [[File:HARICHAUHANBORAZINESIGMA.png|right|200px]]

File:HARICHAUHANBORAZINESIGMA.png

2018-05-25T16:32:02Z

Hc2616:

HariChauhanInorganic

2018-05-25T16:31:25Z

Hc2616: /* Aromaticity */

== BH3 ==

=== B3LYP/6-31G Level ===
[[File:HariChauhan BH3Optimization 6-21G..PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000053 0.001800 YES
RMS Displacement 0.000027 0.001200 YES </pre>

[[Media:HARICHAUHAN_BH3OPTIMIZATION_6-21G_FREQ.log|BH3_frequency.log]]

<pre> Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661 </pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHAN_BH3OPTIMIZATION_6-21G_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'
|slightly
|bend
|-
|1213
|14
|E'
|slightly
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:HariChauhanBH3Spectrum.png|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Only three peaks appear in the predicted spectrum because there are two pairs of E' vibrational modes that are degenerate, hence they appear as one signal each. Furthermore, the A1' symmetric stretch does not produce a change in the dipole moment of the molecule so is not IR active.

[[File:HariChauhanBH3MO2.png|thumb|none|MO diagram for BH3 adapted from provided tutorial sheet|left]]

The a1' molecular orbital looks different from that predicted by LCAO. The s orbitals on the hydrogen atoms appear much larger in the calculated MO. This suggests that the LCAO approach to predicting molecular orbitals may have some inaccuracies.

== NH3 ==

=== B3LYP/6-31G Level ===

[[File:HariChauhanNH3Summary.png]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES</pre>

[[Media:HariChauhanHN3.log|NH3_frequency.log]]

<pre> Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHANNH3.log</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for NH3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1089
|145
|A
|yes
|asymmetric strech
|-
|1693
|14
|E
|slightly
|bend
|-
|1693
|14
|E
|slightly
|bend
|-
|3461
|1
|A1'
|very slightly
|symmetric stretch
|-
|3589
|0
|E
|no
|asymmetric stretch
|-
|3589
|0
|E
|no
|asymmetric stretch
|}

[[File:HARICHAUHANNH3SPECTRUM.LOG|500px|none]]

Similar to BH3, NH3 has two sets of degenerate vibrational modes. However one of these pairs is IR inactive. Therefore, only three signals are predicted in the IR spectrum.

== BH3NH3 ==

=== B3LYP/6-31G Level ===

[[File:HARICHAUHANBH3NH3SUMMARY.PNG|400px]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000350 0.000450 YES
RMS Force 0.000112 0.000300 YES
Maximum Displacement 0.001350 0.001800 YES
RMS Displacement 0.000450 0.001200 YES</pre>

[[Media:HARICHAUHANBH3NH3_OPT.LOG|NH3BH3_frequency.log]]

<pre> Low frequencies --- -0.0262 -0.0082 -0.0023 9.6688 9.6769 37.9651
Low frequencies --- 265.3241 634.4274 639.1700</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHANBH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BH3NH3====
Due to the large number of vibrational modes in BH3NH3, a screenshot of the vibrations predicted by Gaussian is provided. A total of 11 bands should be observed, although some with very low intensity. Also, some are very close in energy so may overlap.

[[File:HARICHAUHANBH3NH3VIBRATIONS.PNG|none|400px]]
[[File:HARICHAUHANBH3NH3SPECTRUM.PNG|none|400px]]

====Calculating B-N Bond Energy in BH3NH3====

<pre>E(NH3)= -56.55777 a.u.
E(BH3)= -26.61532 a.u.
E(NH3BH3)= -83.22469 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.22469 - (-56.55777 - 26.61532) = -0.05167 a.u.

-0.05167 a.u. * 2625 = -136 kJmol-1</pre>

The energy of the B-N bond in BH3NH3 is -136 kJmol-1

Comparing this bond with the C-C bond strength in ethane, which is isoelectronic, the B-N bond is significantly weaker. In ethane, the C-C bond is around 364 kJmol-1, over double that of the B-N bond strength. This is likely due to the large electronegativity difference between B and N.

== BBr3 ==

=== B3LYP/6-31G(d,p)LANL2DZ Level ===
[[File:HARICHAUHANBBR3SUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
</pre>

[[Media:HARICHAUHAN_BBR3OPTIMIZATION.LOG|BBr3_frequency.log]]

<pre> Low frequencies --- -0.0135 -0.0064 -0.0046 2.4669 2.4670 4.8600
Low frequencies --- 155.9626 155.9646 267.7022</pre>

<jmol><jmolApplet>
<title>BBr3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HARICHAUHAN_BBR3OPTIMIZATION.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Vibrational spectrum for BBr3====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|156
|0
|E'
|no
|bend
|-
|156
|0
|E'
|no
|bend
|-
|268
|0
|A1'
|no
|symmetric stretch
|-
|378
|4
|A2"
|slightly
|out-of-plane bend
|-
|763
|320
|E'
|yes
|asymmetric stretch
|-
|763
|320
|E'
|yes
|asymmetric stretch
|}

[[File:HariChauhanBBr3Spectrum.png|none|500px|An IR Spectrum of BBr3 Predicted by Gaussian]]

Only one peak is seen in this spectrum as the two stretches at 763 cm-1 have far higher intensity than the other IR active stretch at 378 cm-1.

{{DOI|10042/202470}}

== Benzene ==

=== B3LYP/6-31G Level ===
[[File:HARICHAUHANBENZENESUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000084 0.000300 YES
Maximum Displacement 0.000767 0.001800 YES
RMS Displacement 0.000328 0.001200 YES</pre>

[[Media:HARICHAUHANBENZENE.LOG|Benzene_frequency.log]]

<pre> Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0054 -0.0054 0.0004
Low frequencies --- 414.1239 414.1239 620.9400</pre>

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

====Vibrational spectrum for Benzene====
[[File:HARICHAUHANBENZENEVIBRATIONS.PNG|500px]]

[[File:HARICHAUHANBENZENESPECTRUM.PNG|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Although benzene clearly has very many vibrational modes, due to its high symmetry, only a few are IR active. This explains why only 4 peaks are observed in its IR spectrum.

== Borazine ==

=== B3LYP/6-31G Level ===
[[File:HARICHAUHANBORAZINESUMMARY.PNG|none|Screenshot of Gaussview Summary]]
<pre> Item Value Threshold Converged?
Maximum Force 0.000443 0.000450 YES
RMS Force 0.000179 0.000300 YES
Maximum Displacement 0.000882 0.001800 YES
RMS Displacement 0.000400 0.001200 YES</pre>

[[Media:HARICHAUHANBORAZINE.LOG|Borazine_frequency.log]]

<pre> Low frequencies --- -0.0045 -0.0033 -0.0031 5.3417 5.3626 5.9709
Low frequencies --- 289.8780 289.8786 404.4105</pre>

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

====Vibrational spectrum for Borazine====
[[File:HARICHAUHANBORAZINEVIBRATIONS.PNG|300px]]

[[File:HARICHAUHANBORAZINESPECTRUM.PNG|none|500px|An IR Spectrum of BH3 Predicted by Gaussian]]

Borazine has the same number of vibrational modes as benzene, however, due to its lower symmetry, more of these are IR active, which is why it shows 6 active signals in the IR spectrum.

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

{| class="wikitable"
|+
|-
|Benzene || Borazine
|-
|[[File:HARICHAUHANBENZENECHARGE.PNG|300px]]
|[[File:HARICHAUHANBORAZINECHARGE.PNG|300px]]
|-
|}

The brighter colours imply a higher magnitude of charge, with red implying a negative charge and green implying a positive charge.

Because carbon and hydrogen have very close electronegativities, the C-H bond has a large amount of covalent character. The C-C bond, being homonuclear, is completely covalent. Therefore, there is little separation of charge in benzene. Because carbon is a little more electronegative than hydrogen, a negative charge of -0.239 resides on the carbon atoms, with +0.239 on the hydrogen atoms. However, due to the D6h point group of the molecule, the sum of the C-H bond dipoles is zero, giving the benzene molecule an overall zero dipole moment.

In borazine, there is a higher separation of charge, shown by the brighter colours in the figure above. Nitrogen has a significantly higher electronegativity than boron and hydrogen, making the N-B and N-H bonds have a large dipole moment. Comparing the B-H and N-H bonds, the hydrogen atoms bonded to boron show little charge but the hydrogen atoms bonded to nitrogen have a charge of +0.432 as electrons in the N-H bond are drawn closer to the nitrogen.

In borazine, a large amount of negative charge resides on the Nitrogen atoms, with the boron and hydrogen atoms having positive charge, however due to the D3h point group of the molecule, the dipole moments of these polar bonds sums to zero, to give borazine no overall dipole moment.

Both molecules have a total charge of zero, so summing up the total charge gives zero in both cases.

===Comparison of Molecular Orbitals===

{| class="wikitable"
|+
|-
|Benzene || Borazine ||Comparison
|-
|style="width: 200pt;" |[[File:HARICHAUHANBENZENEMO12.PNG|300px]]
|style="width: 200pt;" |[[File:HARICHAUHANBORAZINEMO10.PNG|300px]]
|style="width: 500pt;" |MO 12 in benzene and 10 in borazine. Both of these MOs have a large amount of bonding character resulting from overlap of orbitals in the center of the ring in the plane of the molecule. They both result from in-phase overlap of the 1s orbital on hydrogen with the carbon 2p-orbitals along the C-H bonds. In borazine, the 1s on the carbon atoms bonded to boron don't contribute to this MO. This is likely because these hydrogen atoms are roughly neutral, so the 1s electrons are too high in energy to contribute.
|-
|[[File:HARICHAUHANBENZENEMO17.PNG|300px]]
|[[File:HARICHAUHANBORAZINEMO17.PNG|300px]]
|style="width: 500pt;" | MO17 in benzene and borazine. In both benzene and borazine this MO has a large amount of bonding character with a nodal plane in the plane of the molecule. It results from the in phase overlap of the 2p-orbitals adjacent to the ring. In benzene, each carbon contributes equally to this MO giving the MO a C6 rotational axis. In borazine however, there is a slightly larger contribution from the p-orbitals on nitrogen than on boron. This is because the 2p on nitrogen is lower in energy so contributes more to this bonding orbital. This gives this MO a C3 rotational axis.
|-
|[[File:HARICHAUHANBENZENEMO23.PNG|300px]]
|[[File:HARICHAUHANBORAZINEMO23.PNG|300px]]
|style="width: 500pt;" | MO23 in benzene and borazine. These MOs are overall antibonding and result in the out of phase overlap of four p-orbitals perpendicular to the ring. In benzene, each of these 2p-orbitals contributes equally as they are equivalent. In borazine however, the two 2p-orbitals on boron contribute a larger amount than the two 2p-orbitals on nitrogen. This is because this MO is anti-bonding and the 2p on boron are higher in energy than on nitrogen, so are closer in energy to this MO.
|-
|}

== Aromaticity ==

Hückel proposed a few criteria which a molecule must meet in order to be considered aromatic. It must be cyclic, planar, have a continuous system of p-orbitals adjacent to the ring and contain 4n+2 π-electrons in this π-system. This approach to aromaticity suggests that the aromatic stabilization of benzene comes largely from the molecular orbital shown above with an area of electron density above and below the ring of the molecule (MO 17).

However, it is now well known that planarity is not a requirement for aromaticity. At 20K, it has been shown that benzene, in a crystal structure, adopts a chair conformation.<ref>DOI: 10.1002/chem.200700250</ref> In fact, aromaticity is a word used to describe a number of stabilizing effects with the planar π-system being only one of these.

Sigma aromaticity, for example, is displayed in the MO shown. This is caused by the in-phase overlap of p-orbitals in the plane of the ring that face along the B-N bonds. [[Media:HARICHAUHANBORAZINESIGMA.png|right|200px]]

HariChauhanInorganic

2018-05-25T16:31:14Z

HariChauhanInorganic

2018-05-25T14:29:08Z

Hc2616: /* Comparison of Charge */

HariChauhanInorganic

File:HARICHAUHANBORAZINESPECTRUM.PNG

2018-05-24T20:28:42Z

Hc2616: