ChemWiki - User contributions [en]

Rep:Mod:LJK27

2018-05-25T15:15:37Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment of the colour on the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B.

There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. The electronegativity according to the Pauling scale is given as 2.04 for boron and 3.04 for nitrogen. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms. B and N have a large difference in charge resulting in ionic character of bonds; all the ring atoms in benzene are carbon and so have an equal share of charge.

Similarly the H atoms attached to B atoms are less intense in charge than those attached to N atoms due to a greater difference in electronegativity between N and H compared to B and H.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are two nodes in both MOs due to changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less than the nitrogen atoms, and therefore the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine have a contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals, and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic concept of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current (indicating delocalisation), it obeys the 4n + 2 rule, and all BN bond lengths are equal. The (4n + 2) pi electron rule is used for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:14:51Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment of the colour on the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B.

There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. The electronegativity according to the Pauling scale is given as 2.04 for boron and 3.04 for nitrogen. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms. B and N have a large difference in charge resulting in ionic character of bonds; all the ring atoms in benzene are carbon and so have an equal share of charge.

Similarly the H atoms attached to B atoms are less intense in charge than those attached to N atoms due to a greater difference in electronegativity between N and H compared to B and H.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are two nodes in both MOs due to changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less than the nitrogen atoms, and therefore the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine have a contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals, and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic concept of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current (indicating delocalisation), it obeys the 4n + 2 rule, and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:13:56Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment of the colour on the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B.

There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. The electronegativity according to the Pauling scale is given as 2.04 for boron and 3.04 for nitrogen. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms. B and N have a large difference in charge resulting in ionic character of bonds; all the ring atoms in benzene are carbon and so have an equal share of charge.

Similarly the H atoms attached to B atoms are less intense in charge than those attached to N atoms due to a greater difference in electronegativity between N and H compared to B and H.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are two nodes in both MOs due to changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less than the nitrogen atoms, and therefore the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine have a contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals, and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic concept of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:13:25Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment of the colour on the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B.

There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. The electronegativity according to the Pauling scale is given as 2.04 for boron and 3.04 for nitrogen. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms. B and N have a large difference in charge resulting in ionic character of bonds; all the ring atoms in benzene are carbon and so have an equal share of charge.

Similarly the H atoms attached to B atoms are less intense in charge than those attached to N atoms due to a greater difference in electronegativity between N and H compared to B and H.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are two nodes in both MOs due to changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less than the nitrogen atoms, and therefore the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine have a contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals, and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:12:14Z

Ljk16: /* Molecular Orbitals for Benzene and Borazine */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment of the colour on the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B.

There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. The electronegativity according to the Pauling scale is given as 2.04 for boron and 3.04 for nitrogen. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms. B and N have a large difference in charge resulting in ionic character of bonds; all the ring atoms in benzene are carbon and so have an equal share of charge.

Similarly the H atoms attached to B atoms are less intense in charge than those attached to N atoms due to a greater difference in electronegativity between N and H compared to B and H.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are two nodes in both MOs due to changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less than the nitrogen atoms, and therefore the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine have a contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:10:23Z

Ljk16: /* Charge Distribution */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment of the colour on the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B.

There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. The electronegativity according to the Pauling scale is given as 2.04 for boron and 3.04 for nitrogen. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms. B and N have a large difference in charge resulting in ionic character of bonds; all the ring atoms in benzene are carbon and so have an equal share of charge.

Similarly the H atoms attached to B atoms are less intense in charge than those attached to N atoms due to a greater difference in electronegativity between N and H compared to B and H.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:09:17Z

Ljk16: /* Charge Distribution */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment of the colour on the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. The electronegativity according to the Pauling scale is given as 2.04 for boron and 3.04 for nitrogen. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms. B and N have a large difference in charge resulting in ionic character of bonds; all the ring atoms in benzene are carbon and so have an equal share of charge.

Similarly the H atoms attached to B atoms are less intense in charge than those attached to N atoms due to a greater difference in electronegativity between N and H compared to B and H.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:07:11Z

Ljk16: /* Charge Distribution */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment of the colour on the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. The electronegativity according to the Pauling scale is given as 2.04 for boron and 3.04 for nitrogen. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms. B and N have a large difference in charge resulting in ionic character of bonds; all the ring atoms in benzene are carbon and so have an equal share of charge.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:01:33Z

Ljk16: /* Borazine */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:01:02Z

Ljk16: /* Benzene */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T15:00:33Z

Ljk16: /* BBr3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T14:59:52Z

Ljk16: /* NH3BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T14:59:35Z

Ljk16: /* NH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T14:59:07Z

Ljk16: /* BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

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

The frequencies are outside the 15 cm-1 range but this was discussed with a demonstrator and deemed fine as the calculation converged.

<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T14:56:07Z

Ljk16: /* BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity (arbitrary units) !! Symmetry !! IR active? !! Type
|-
| 1164 || 92 || A2" || Yes || Bend
|-
| 1214 || 14 || E' || Very slight || Bend
|-
| 1214 || 14 || E' || Very Slight || Bend
|-
| 2580 || 0 || A1' || No || Symmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|-
| 2713 || 126 || E' || Yes || Asymmetric stretch
|}

The three vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The three vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment, and therefore does not appear in the IR spectrum.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T14:45:57Z

Ljk16: /* BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T14:44:15Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. The MOs lowest in energy have fewer nodes and greatest orbital overlap. This relates to the basic conception of aromaticity arising as a result of pz AO overlap.

The concept of overlapping pz AOs is a bad description for aromaticity. The pi-electron delocalisation was initially the explanation of aromatic stabilisation. However, there has been suggestion that the sigma electrons also have a role in aromatic stabilisation. The initial definition of aromaticity was for planar structures and the overlap of perpendicular p orbitals but it is now recognised that aromatic structures do not have to be planar.<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings" /> Also aromaticity can be used to describe non-carbon structures such as metallic clusters where these associated properties are seen. Borazine can be described as weakly aromatic with a small ring current indicating delocalisation, it obeys the 4n + 2 rule and all BN bond lengths are equal. The (4n + 2) pi electron rule for indicating if something is aromatic. This is useful as the electronic structure is fundamental in determining the properties and ultimately aromaticity of a compound.<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters" />

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
<ref name="Application of AIM Parameters at Ring Critical Points for Estimation of p-Electron Delocalization in Six-Membered Aromatic and Quasi-Aromatic Rings">M. Palusiak and T. Krygowski, Chemistry. A European Journal.</ref>
<ref name="Phenomenological Shell Model and Aromaticity in Metal Clusters">T. Holtzl, T. Veszpremi, M. T. Nguyen and P. Lievens, Research Gate, 2009.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T14:14:15Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. There is an aromatic stabilisation energy which has been shown experimentally by comparisons to hydrogenation of cyclohexene to benzene. When placed in an applied magnetic field a pi ring current is induced and a magnetic field is induced by the ring current as a result of electron movements within orbitals and there is resulting diamagnetic anisotropy. There is a difference in the field experienced by the protons; protons outside the ring experience low field and protons inside the ring experience high field. It is unfavourable for aromatics to lose there resonance stabilisation energy so in reactions with bromine water no decolourisation is observed.

The real MOs show the delocalisation and overlapping of orbitals when the phase is the same, as in MO17 above. These are the MOs lowest in energy. There is the (4n + 2) pi electron rule for indicating if something is aromatic.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:41:46Z

Ljk16: /* Molecular Orbitals for Benzene and Borazine */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO17 for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO21 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO15 for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. The

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:40:47Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

Aromaticity was historically described by Kekule as resembling benzene. Properties associated with aromaticity are the intermediate lengths between single and double bonds between the ring atoms, for example in benzene the carbon-carbon bond lengths. The

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:34:50Z

Ljk16: /* Molecular Orbitals for Benzene and Borazine */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO17 for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO21 for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO14 for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

Aromaticity was

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:33:09Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

Aromaticity was

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:31:41Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:31:19Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

''''References''''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:30:45Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

''References''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:30:31Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition, Page 365.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969.</ref>
</references>

Rep:Mod:LJK27

2018-05-25T13:29:43Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T13:08:24Z

Ljk16: /* Molecular Orbitals for Benzene and Borazine */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO20 for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:57:01Z

Ljk16: /* Borazine */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>Borazine</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:56:42Z

Ljk16: /* Benzene */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>Benzene</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:56:21Z

Ljk16: /* BBr3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>BBr3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:55:58Z

Ljk16: /* NH3BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:55:40Z

Ljk16: /* NH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3 adduct</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:55:20Z

Ljk16: /* BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>BH3</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3 adduct</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:54:29Z

Ljk16: /* Charge Distribution */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3 adduct</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:54:12Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3 adduct</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

Charge - Hartrees?

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc, 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:53:52Z

Ljk16: /* Concept of Aromaticity */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3 adduct</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

Charge - Hartrees?

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references>
<ref name="BN dative bond">Weller, Overton, Rourke and Armstrong, Inorganic Chemistry, 6th Edition.</ref>
<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO">D.R. Armstrong and P. G. Perkins, J. Chem. Soc 1969
</references>

Rep:Mod:LJK27

2018-05-25T12:53:30Z

Ljk16: /* NH3BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3 adduct</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar.<ref name="BN dative bond" /> The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond.<ref name="Calculation of the Electronic Structures and the Gas-phase Heats of Formation of BH3,NH3 and BH3,CO" /> This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

Charge - Hartrees?

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references />

Rep:Mod:LJK27

2018-05-25T12:40:54Z

Ljk16: /* NH3BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>NH3BH3 adduct</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55777 au
•E(BH3)= -26.61532 au
•E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -129 kJ/mol

Thus we need to report energies in au up to an accuracy of 1 kJ/mol, making the conversion this is 0.0004 au, so report energies in au up to 5dp (to avoid rounding errors)

B-N is a fairly strong dative bond. NH3BH3 is a solid at room temperature whereas analogous ethane is a gas which is due to ammonia-borane having a large dipole moment and ethane being non-polar. The association energy for BH3CO is -90.5 kJ/mol which is less than NH3BH3's association energy which again supports B-N being a strong dative bond. This is owing to the large difference in electronegativities of boron and nitrogen.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

Charge - Hartrees?

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references />

Rep:Mod:LJK27

2018-05-25T10:47:51Z

Ljk16: /* IR Spectrum for BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || A2"
|-
| 1214 || 14 || E'
|-
| 1214 || 14 || E'
|-
| 2580 || 0 || A1'
|-
| 2713 || 126 || E'
|-
| 2713 || 126 || E'
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55776873 au
•E(BH3)= -26.61532342 au
•E(NH3BH3)= -83.22468990 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -128.994375 kJ/mol

Thus we need to report energies in au up to an accuracy of 1 kJ/mol, making the conversion this is 0.0004 au, so report energies in au up to 5dp (to avoid rounding errors)

B-N is a weak dative bond.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

Charge - Hartrees?

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references />

Rep:Mod:LJK27

2018-05-24T22:09:56Z

Ljk16: /* Molecular Orbital Diagram for BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || bend
|-
| 1214 || 14 || bend
|-
| 1214 || 14 || bend
|-
| 2580 || 0 || symmetric stretch?
|-
| 2713 || 126 || asymmetric stretch
|-
| 2713 || 126 || asymmetric stretch
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55776873 au
•E(BH3)= -26.61532342 au
•E(NH3BH3)= -83.22468990 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -128.994375 kJ/mol

Thus we need to report energies in au up to an accuracy of 1 kJ/mol, making the conversion this is 0.0004 au, so report energies in au up to 5dp (to avoid rounding errors)

B-N is a weak dative bond.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

Charge - Hartrees?

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references />

Rep:Mod:LJK27

2018-05-24T22:09:31Z

Ljk16: /* Molecular Orbital Diagram for BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || bend
|-
| 1214 || 14 || bend
|-
| 1214 || 14 || bend
|-
| 2580 || 0 || symmetric stretch?
|-
| 2713 || 126 || asymmetric stretch
|-
| 2713 || 126 || asymmetric stretch
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|800px]]

Talk about how LCAO compare to the real MOs.....•Are there any significant differences between the real and LCAO MOs?
•What does this say about the accuracy and usefulness of qualitative MO theory?

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55776873 au
•E(BH3)= -26.61532342 au
•E(NH3BH3)= -83.22468990 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -128.994375 kJ/mol

Thus we need to report energies in au up to an accuracy of 1 kJ/mol, making the conversion this is 0.0004 au, so report energies in au up to 5dp (to avoid rounding errors)

B-N is a weak dative bond.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

Charge - Hartrees?

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references />

Rep:Mod:LJK27

2018-05-24T22:09:14Z

Ljk16: /* Molecular Orbital Diagram for BH3 */

== BH3 ==

Calculation Method: B3LYP
Basis set: 3-21G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

What definition would you choose for the existence of a bond?

Calculation method: B3LYP
Basis set: 6-31G

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

[[File:BH3_summary_ljk27_best.png]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>
<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LARA_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:LARA_BH3_FREQ.LOG]]

===IR Spectrum for BH3===

[[File:bh3_ir_spectrum_ljk27.png|600px]]
[[File:bh3_ir_stretches_ljk27.png| 300px]]

{| class="wikitable" border="1"
! Vibrations (cm-1) !! Intensity !! Symmetry
|-
| 1164 || 92 || bend
|-
| 1214 || 14 || bend
|-
| 1214 || 14 || bend
|-
| 2580 || 0 || symmetric stretch?
|-
| 2713 || 126 || asymmetric stretch
|-
| 2713 || 126 || asymmetric stretch
|}

The two vibrations at 1214 and at 1164 cm-1 are angle deformations because the angle around the bond is changing but the length of the bond stays the same. The two vibrations at 2713 and at 2580 cm-1 are bond stretches as the bond elongates and then retracts. The two 1214 cm-1, and two 2713 cm-1 vibrations are degenerate as they have the same wavenumber (which is proportional to the energy). The degenerate stretches appear as one peak in the spectrum which is why there are less than 6 peaks observed even though there are six vibrations. The symmetric stretch at 2580 cm-1 is IR inactive since there is no change in dipole moment.
Vibrations with very low intensity will not be experimentally observable. This includes 2580 cm-1 with an intensity of zero and the degenerate 1214 cm-1 angle deformations, with intensities of approximately 14 cm-1.

===Molecular Orbital Diagram for BH3===

[[File:complete_bh3_mo1_ljk27.png|600px]]

Talk about how LCAO compare to the real MOs.....•Are there any significant differences between the real and LCAO MOs?
•What does this say about the accuracy and usefulness of qualitative MO theory?

The real MO at the bottom left of the MO diagram is the bonding 1s boron MO.

The shaded negative phase in the LCAO MOs correspond to green regions in the real MOs, and unshaded positive phase to red regions.
The real MOs appear to cover a larger surface area of the molecule than the LCAOs. For example, a1' in the LCAO doesn't suggest the delocalisation of this MO as can be seen in the real MO for a1'. However, the LCAO shows the composition of the MO more clearly and so it is useful in indicating which atomic orbitals are in combination in order to form that MO. The approximate shape of the LCAOs and real MOs are fairly similar, however there is less of a difference in shape between the s and p orbitals in the real MOs which can make it difficult to distinguish the real MOs; this is a benefit of the LCAOs.

== NH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

[[File:nh3_summary_ljk27.png]]

<pre>
Low frequencies --- -34.7257 -34.7136 -21.3130 -0.0033 0.0071 0.0474
Low frequencies --- 1089.3593 1694.0550 1694.0553
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3_2_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3_2_FREQ_LJK27.LOG]]

== NH3BH3 ==
Calculation method: B3LYP
Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000207 0.000450 YES
RMS Force 0.000079 0.000300 YES
Maximum Displacement 0.001006 0.001800 YES
RMS Displacement 0.000524 0.001200 YES
</pre>

[[File:nh3bh3_opt_summ_ljk27.png]]

<pre>
Low frequencies --- -0.0584 -0.0503 -0.0074 21.5681 21.5784 37.7476
Low frequencies --- 264.2274 631.7078 639.2561
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3_FREQ_LJK27.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[File:NH3BH3_FREQ_LJK27.LOG]]

•E(NH3)= -56.55776873 au
•E(BH3)= -26.61532342 au
•E(NH3BH3)= -83.22468990 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]= -0.05160 au (5dp) = -128.994375 kJ/mol

Thus we need to report energies in au up to an accuracy of 1 kJ/mol, making the conversion this is 0.0004 au, so report energies in au up to 5dp (to avoid rounding errors)

B-N is a weak dative bond.

== BBr3 ==
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
</pre>

[[File:LJK27_BBr3_2_opt_summ.png]]

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

[[File:LJK27_BBr3_freq_2.png]]

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>LJK27_BBr3_2_frequency.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:LJK27_BBr3_2_frequency.log]]

{{DOI|10042/202464}}

== Aromaticity: Benzene and Borazine ==
===Benzene===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000198 0.000450 YES
RMS Force 0.000076 0.000300 YES
Maximum Displacement 0.000812 0.001800 YES
RMS Displacement 0.000283 0.001200 YES
</pre>

[[File:benzene_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -2.1456 -2.1456 -0.0089 -0.0043 -0.0043 10.4835
Low frequencies --- 413.9768 413.9768 621.1390
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>benzene_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:benzene_freq_ljk27.log]]

===Borazine===
Calculation method: B3LYP

Basis set: 6-31G

<pre>
Item Value Threshold Converged?
Maximum Force 0.000165 0.000450 YES
RMS Force 0.000049 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
</pre>

[[File:borazine_opt_ljk27_summ.png]]

<pre>
Low frequencies --- -8.1143 -7.7640 -7.4910 -0.0099 -0.0082 0.1221
Low frequencies --- 289.0794 289.0902 403.3679
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>borazine_freq_ljk27.log</uploadedFileContents>
</jmolApplet></jmol>

[[File:borazine_freq_ljk27.log]]

===Charge Distribution===

[[File:benzene_charge1_ljk27.png|210px|thumb| A Gaussview image of benzene labelled with its charges.]]

[[File:borazine_charge_ljk27.png|210px|thumb| A Gaussview image of borazine labelled with its charges.]]

The images represent the charge distribution of benzene and borazine. The same colour range was used to visualise the charge intensity by corresponding to the pigment intensity of the colour of the atoms. Borazine has more intense colours and thus more intense charge on the individual atoms. Benzene has a more even spread of charge with a value of +0.239 on the H atoms and -0.239 on the C atoms. The more electronegative atoms have a more negative value of charge located on them than the more electropositive atoms. Therefore, in borazine the N atom has a value of -1.102, +0.432 on H and +0.747 on B. There is a greater difference in electronegativities in borazine than in benzene, and thus a less even spread of charge due to the alterating ring atoms in borazine. Most of the charge located in borazine is located on ring atoms as can be seen in the image with the H atoms being much duller than the B and N atoms.

Charge - Hartrees?

===Molecular Orbitals for Benzene and Borazine===
{| class="wikitable" border="1"
|+ caption
! Benzene !! Borazine !! Description
|-
| [[File:benzene_mo1_ljk27.png|200px]] || [[File:borazine_mo1_ljk27.png|200px]] || MO? for benzene and MO? for borazine are very similar. Both MOs have antibonding character with a positive phase above the ring and negative phase below the ring giving an asymmetric phase with one node. These are moderlately low energy bonding MOs. The contributions are from the ring atoms, carbon in benzene and boron and nitrogen atoms in borazine, but there is not a significant contribution from H atoms.
|-
| [[File:benzene_mo2_ljk27.png|200px]] || [[File:borazine_mo3_ljk27.png|200px]] || MO? for benzene and MO? for borazine show similar bondng character. There are to nodes in both MOs with changes in phase. Benzene has slightly larger electron clouds and equal contributions from all ring atoms which demonstrates that this benzene MO is very delocalised. The boron atoms in borazine contribute less and the MO is less symmetric.
|-
| [[File:benzene_mo4_ljk27.png|200px]] || [[File:borazine_mo5_ljk27.png|200px]] || MO? for benzene and MO? for borazine both have some contribution from all of the atoms in the molecule except for two hydrogen atoms on opposite sides of the ring. Both MOs have two nodes with elements of antibonding character. The benzene MO has greater symmetry whereas in borazine there is greater delocalisation around nitrogen atoms than from the boron atoms owing to differences in electronegativity.
|}

===Concept of Aromaticity===
discuss in your wiki (2-3 paragraphs) the concept of aromaticity, the simple ideas and also the more complex descriptions.
how do the real MOs relate to the common (very basic) conceptions of aromaticity?
you are expected to explain why the concept of overlapping pz AOs is NOT a good description for aromaticity.

'''References'''
<references />

Rep:Mod:LJK27

2018-05-24T21:55:46Z

Ljk16: /* Charge Distribution */

Rep:Mod:LJK27

2018-05-24T21:54:29Z

Ljk16: /* Concept of Aromaticity */

Rep:Mod:LJK27

2018-05-24T21:52:28Z

Ljk16: /* IR Spectrum for BH3 */

Rep:Mod:LJK27

2018-05-24T21:47:38Z

Ljk16: /* IR Spectrum for BH3 */

Rep:Mod:LJK27

2018-05-24T21:35:54Z

Ljk16: /* IR Spectrum for BH3 */

Rep:Mod:LJK27

2018-05-24T21:31:59Z

Ljk16: /* IR Spectrum for BH3 */

Rep:Mod:LJK27

2018-05-24T21:31:21Z

Ljk16: /* IR Spectrum for BH3 */