ChemWiki - User contributions [en]

User:Molecular Modelling (jr1416)

2018-05-11T14:18:06Z

Jr1416: /* Discussion */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Animation Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

=== Charge Table ===

{| class="wikitable"
|-
!
! Hydrogen
! Carbon
! Nitrogen
! Boron
|-
| Benzene
| 0.239
| -0.239
|
|
|-
| Borazine
| 0.432 / -0.077
|
| -1.102
| 0.747
|}

=== Discussion ===

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 <ref>Revised Mulliken electronegativities: I. Calculation and conversion to Pauling units
Steven G. Bratsch
Journal of Chemical Education 1988 65 (1), 34
DOI: 10.1021/ed065p34</ref>and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average delocalised pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from combining in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for neutral homocyclics like benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity<ref>Application of AIM Parameters at Ring Critical Points for Estimation ofp-Electron Delocalization in Six-Membered Aromatic andQuasi-Aromatic Rings, Dr. M. Palusiak, Prof. Dr. T. M. Krygowski, DOI: 10.1002/chem.200700250</ref>. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, suggesting that the aromaticity should be broken, however it isn't and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above. This molecular orbital clearly shows the a delocalised MO produced from the overlap of all of the s-orbitals, a similar MO is also produced in borazine's analogous MO. This shows that the basic interpretation of overlapping pz orbitals is not enough to explain the complex factors involved with the aromaticity of a molecule, instead calculations of MOs is a better method for visualising and understanding aromaticity.

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T14:15:59Z

Jr1416: /* Discussion on Aromaticity */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Animation Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

=== Charge Table ===

{| class="wikitable"
|-
!
! Hydrogen
! Carbon
! Nitrogen
! Boron
|-
| Benzene
| 0.239
| -0.239
|
|
|-
| Borazine
| 0.432 / -0.077
|
| -1.102
| 0.747
|}

=== Discussion ===

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average delocalised pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from combining in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for neutral homocyclics like benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity<ref>Application of AIM Parameters at Ring Critical Points for Estimation ofp-Electron Delocalization in Six-Membered Aromatic andQuasi-Aromatic Rings, Dr. M. Palusiak, Prof. Dr. T. M. Krygowski, DOI: 10.1002/chem.200700250</ref>. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, suggesting that the aromaticity should be broken, however it isn't and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above. This molecular orbital clearly shows the a delocalised MO produced from the overlap of all of the s-orbitals, a similar MO is also produced in borazine's analogous MO. This shows that the basic interpretation of overlapping pz orbitals is not enough to explain the complex factors involved with the aromaticity of a molecule, instead calculations of MOs is a better method for visualising and understanding aromaticity.

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T14:10:13Z

Jr1416: /* Table */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Animation Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

=== Charge Table ===

{| class="wikitable"
|-
!
! Hydrogen
! Carbon
! Nitrogen
! Boron
|-
| Benzene
| 0.239
| -0.239
|
|
|-
| Borazine
| 0.432 / -0.077
|
| -1.102
| 0.747
|}

=== Discussion ===

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average delocalised pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from combining in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for neutral homocyclics like benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, suggesting that the aromaticity should be broken, however it isn't and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above. This molecular orbital clearly shows the a delocalised MO produced from the overlap of all of the s-orbitals, a similar MO is also produced in borazine's analogous MO. This shows that the basic interpretation of overlapping pz orbitals is not enough to explain the complex factors involved with the aromaticity of a molecule, instead calculations of MOs is a better method for visualising and understanding aromaticity.

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T14:08:58Z

Jr1416: /* Charge Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

{| class="wikitable"
|-
!
! Hydrogen
! Carbon
! Nitrogen
! Boron
|-
| Benzene
| 0.239
| -0.239
|
|
|-
| Borazine
| 0.432 / -0.077
|
| -1.102
| 0.747
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average delocalised pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from combining in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for neutral homocyclics like benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, suggesting that the aromaticity should be broken, however it isn't and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above. This molecular orbital clearly shows the a delocalised MO produced from the overlap of all of the s-orbitals, a similar MO is also produced in borazine's analogous MO. This shows that the basic interpretation of overlapping pz orbitals is not enough to explain the complex factors involved with the aromaticity of a molecule, instead calculations of MOs is a better method for visualising and understanding aromaticity.

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T14:08:31Z

Jr1416: /* Charge Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

{| class="wikitable"
|-
!
! Hydrogen
! Carbon
! Nitrogen
! Boron
|-
| Benzene
| 0.239
| -0.239
|
|
|-
| Borazine
| 0.432/-0.077
|
| -1.102
| 0.747
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average delocalised pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from combining in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for neutral homocyclics like benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, suggesting that the aromaticity should be broken, however it isn't and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above. This molecular orbital clearly shows the a delocalised MO produced from the overlap of all of the s-orbitals, a similar MO is also produced in borazine's analogous MO. This shows that the basic interpretation of overlapping pz orbitals is not enough to explain the complex factors involved with the aromaticity of a molecule, instead calculations of MOs is a better method for visualising and understanding aromaticity.

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T14:02:33Z

Jr1416: /* Discussion on Aromaticity */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average delocalised pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from combining in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for neutral homocyclics like benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, suggesting that the aromaticity should be broken, however it isn't and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above. This molecular orbital clearly shows the a delocalised MO produced from the overlap of all of the s-orbitals, a similar MO is also produced in borazine's analogous MO. This shows that the basic interpretation of overlapping pz orbitals is not enough to explain the complex factors involved with the aromaticity of a molecule, instead calculations of MOs is a better method for visualising and understanding aromaticity.

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T13:49:29Z

Jr1416: /* Discussion on Aromaticity */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from its overlapping in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for neutral homocyclics like benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, it also means that the p-orbitals will not be able to overlap as efficiently and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above. This molecular orbital clearly shows the a delocalised MO produced from the overlap of all of the s-orbitals, a similar MO is also produced in borazine's analogous MO.

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T13:38:37Z

Jr1416: /* Discussion on Aromaticity */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from its overlapping in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for neutral homocyclics like benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, it also means that the p-orbitals will not be able to overlap as efficiently and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above. This molecular orbital clearly shows the a delocalised MO produced from the overlap of all of the s-orbitals, a similar MO is also produced in borazine's analogous MO. Another point at which the original theory breaks down is in the case of Quasi-aromatic compounds such as

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T13:30:48Z

Jr1416: /* Discussion on Aromaticity */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from its overlapping in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO) which works for benzene at room temperature but later we will see why this model falls apart for aromaticity as a whole.

With more powerful computational methods available to us now it has been discovered that benzene at 20 K adopts a boat conformation, whilst retaining its aromaticity. This definitively breaks Huckels rule that the ring needs to be planar to be aromatic, it also means that the p-orbitals will not be able to overlap as efficiently and therefore there must be other factors contributing to the aromaticity of the molecule. The reasoning behind this is thought to be due to the aromaticity actually having a contribution from s-orbitals as well as overlapping p-orbitals, which can be visualised by looking at the 7th molecular orbital of benzene above.

== References ==

User:Molecular Modelling (jr1416)

2018-05-11T13:18:02Z

Jr1416: /* Discussion on Aromaticity */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

Aromaticity was first identified by Kekule with respect to the molecule of benzene, his model suggested interchanging double bonds around the ring, which changed so rapidly that an average pseudo-structure is observed. This theory has since been updated many times, to the quantitative rules that we know as Huckels rules for aromaticity; 4n+2 p electrons, planar contiguous ring, orthogonal p orbitals to ring plane. These guidelines rely on the aromaticity of a compound being derived from its overlapping in phase pz atomic orbitals from the linear combination of atomic orbitals theory (LCAO)

== References ==

User:Molecular Modelling (jr1416)

2018-05-10T20:54:15Z

Jr1416: /* Molecular Orbital Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
! MO description
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

== References ==

User:Molecular Modelling (jr1416)

2018-05-10T20:53:20Z

Jr1416: /* Molecular Orbital Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
!
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

== References ==

User:Molecular Modelling (jr1416)

2018-05-10T20:52:27Z

Jr1416: /* Molecular Orbital Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
!
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

== References ==

User:Molecular Modelling (jr1416)

2018-05-10T20:51:47Z

Jr1416: /* Molecular Orbital Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
!
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
π bonding MOs with 1 node
|-
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

== References ==

User:Molecular Modelling (jr1416)

2018-05-10T20:50:40Z

Jr1416: /* Molecular Orbital Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
!
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
| produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the | |
| borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
| means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
| the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
| overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
| benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
| energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
| MO.
|-
|}

== Discussion on Aromaticity ==

== References ==

User:Molecular Modelling (jr1416)

2018-05-10T20:49:17Z

Jr1416: /* Molecular Orbital Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
!
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the borazine
MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals,
means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of
the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p
overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The
benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower
energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the
MO.
|-
|}

== Discussion on Aromaticity ==

== References ==

User:Molecular Modelling (jr1416)

2018-05-10T20:48:05Z

Jr1416: /* Molecular Orbital Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

=== Summary Table ===

[[File:BH3_summary_table(jr1416).PNG]]

=== Item Table ===

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

=== Frequency Analysis ===

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

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

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

=== Infrared Vibrational Analysis ===

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|}

=== IR Spectrum ===

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

=== Molecular Orbitals ===

[[File:Final_BH3_MO(jr1416).PNG]]

Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

==== Item Table ====

<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>

==== Log File ====

[[Media:JR_NH3_VIB.LOG|JR_NH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3_optimization_Summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

==== Item Table ====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

==== Log File ====

[[Media:JR_NH3BH3_VIB.LOG|JR_NH3BH3_VIB.LOG]]

==== Summary Table ====

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

==== Frequency Analysis ====

<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

==== Animation ====

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Energy ====

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 Energy of Reaction ===

==== Calculation ====

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

==== Interpretation ====

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p), for the Boron atom, and LANL2DZ, for the Bromine atoms, was used to calculate and optimise the structure of BBr3.

=== Item Table ===

<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>

=== Log File ===

[[Media:JR_BBr3_VIB_2.log|JR_BBr3_VIB_2.log]]

=== Summary Table ===

[[File:JR_BBr3_Summary_table_2.PNG]]

=== Frequency Analysis ===

Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

=== Animation ===

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

=== DSpace link ===

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

The Method used for the optimisation of Benzene is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

=== Summary Table ===

[[File:Benzene_Summary_table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BENZENE_SYM_FREQ.LOG|JR_BENZENE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

The Method used for the optimisation of Borazine is RB3LYP and the basis set used is 6-31G(d,p).

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

=== Summary Table ===

[[File:Borazine_Summary_Table(jr1416).PNG]]

=== Log File ===

[[Media:JR_BORAZINE_SYM_FREQ.LOG|JR_BORAZINE_SYM_FREQ.LOG]]

=== Frequency Analysis ===

Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

=== Animation ===

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

=== Table ===

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

The benzene charge distribution shows a symmetrical arrangement of the charge with the more electronegative carbon, Mulliken electronegativity 2.55, having a charge of -0.239 and the more electropositive hydrogen, Mulliken electronegativity 2.2, having a charge of 0.239. Compared with borazine, there is a relatively low charge distribution in benzene due to the lower polarity between carbon and hydrogen. Each carbon and each hydrogen has the same partial charge, creating a negatively inner ring which is susceptible to electrophilic attack.

The borazine NBO analysis shows that there is a high distribution of charge with the highly electronegative nitrogen, Mulliken electronegativity 3.04, compared with the electropositive boron, Mulliken electronegative 2.04, giving a polar bond which results in borazine having an alternating charge distribution (N=-1.102, B= 0.747) in the inner ring. This makes the ring susceptible to electrophilic attack at the nitrogen and nucleophilic attack at the boron on the ring. Due to the differing electronegativities of the inner ring substituent atoms, two hydrogen charge environments are produced. Hydrogen has a Mulliken electronegativity of 2.2 and therefore is more electronegative than boron, giving each hydrogen bonded to a boron a charge of -0.077, whilst nitrogen is more electronegative than hydrogen resulting in nitrogen bound hydrogens a charge of 0.432.

{| class="wikitable"
|-
! Structure
! Inner ring charge
! Reactivity of ring
! Hydrogen environments
|-
| Benzene
| Negative
| Electrophilic attack on C
| 1
|-
| Borazine
| Positive on B, Negative on N
| Nucleophilic attack on B, Electrophilic attack on N
| 2
|}

=== Analysis ===

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
!
! Benzene MO
! Borazine MO
! Comments
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px| MO 7 ]]
| [[File:Borazine_MO_1(jr1416).PNG|300px| MO 7 ]]
| These are MOs 7 for both benzene and borazine, they are both completely in phase sigma bonding molecular orbitals. Benzene shows an MO comprised of the 1s hydrogen orbitals and 2s carbon orbitals overlapping in phase to
produce a bonding orbital, whilst in the analogous borazine MO, there is only overlap between the 2s of the nitrogen atomic orbitals and the 1s of the hydrogens attached to these. This results in the raising in energy of the borazine MO, as there is less delocalisation due to the poor energy match between the 2s boron and nitrogen atomic orbitals leaving the 2s of the boron and attached hydrogens out of the MO.
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px| MO 20 ]]
| [[File:Borazine_MO_2(jr1416).PNG|300px| MO 20 ]]
| These are MOs 20 for both benzene and borazine, they are both π bonding orbitals with 1 node across the centre of the molecule. The high symmetry of the benzene molecule, with all carbons having equal energy 2p orbitals, means that there are equal sized molecular orbitals with 1 nodal plane, whilst the borazine MO shows a 2 different sized MOs due to the lower symmetry of the molecule and the energy differences of the 2p orbitals. The larger of the 2 in phase π clouds in the borazine molecule is attributed to the N-B-N 2p overlap, due to nitrogens 2p orbitals being lower in energy and thus contributing more to the bonding MO, the smaller is attributed to the B-N-B 2p overlap.
|-
| π anti-bonding MOs with 2 nodes
| [[File:Benzene_MO_3(jr1416).PNG|300px| MO 23 ]]
| [[File:Borazine_MO_3(jr1416).PNG|300px| MO 23 ]]
| These are MOs 23 for both benzene and borazine, they are both π anti-bonding orbitals with 2 nodal planes at right angles to one another creating 2 in phase 2p-2p orbital overlap MO clouds and 2 out of phase 2p MO clouds. The benzene molecule due to its equal energy of all the C 2p orbitals maintains 2 same sized out of phase p-orbitals and 2 in phase 2p-2p orbital MO clouds. Whilst the borazine contains N which give larger orbitals due to lower energy 2p orbitals, the larger out of phase p-orbital is due to a nitrogen 2p orbital, the smaller due to boron, both the overlapping in phase 2p-2p MO clouds are due to B-N 2p overlap and thus have the same contribution to the MO.
|-
|}

== Discussion on Aromaticity ==

== References ==

User:Molecular Modelling (jr1416)

2018-05-10T19:33:36Z

Jr1416: /* Charge Analysis */

User:Molecular Modelling (jr1416)

2018-05-10T13:17:17Z

Jr1416:

User:Molecular Modelling (jr1416)

2018-05-10T13:05:25Z

2018-05-10T12:38:34Z

Jr1416: /* Charge Analysis */

== BH3 section ==

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of BH3.

[[File:BH3_summary_table(jr1416).PNG]]

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

Frequency analysis log file [[Media:JR_BH3_FREQ.LOG| JR_BH3_FREQ.LOG]]

<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>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BH3_FREQ.mol</uploadedFileContents>
</jmolApplet></jmol>

{| class="wikitable"
|-
! Mode
! Frequency (cm-1)
! Intensity
! Symmetry
! IR activity
! Type of vibration
|-
| 1
| 1160
| 92
| A2"
| Active
| Out of plane bend
|-
| 2
| 1210
| 14
| E'
| Active
| Bend
|-
| 3
| 1210
| 14
| E'
| Active
| Bend
|-
| 4
| 2580
| 0
| A1'
| Inactive
| Symmetric Stretch
|-
| 5
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-
| 6
| 2710
| 126
| E'
| Active
| Asymmetric stretch
|-

|}

[[File:BH3_IR_spectrum(jr1416).PNG]]

The number of peaks corresponds to the number of non-degenerate IR active peaks, this is why only 3 peaks are seen in the computed spectrum. Only these modes provide a change in dipole moment of the molecule, a requirement for absorption of a photon.

[[File:Final_BH3_MO(jr1416).PNG]]

The real MO's are more diffuse than the LCAO's and also have the constructive and destructive phase overlaps as well. The qualitative MO's are a good estimate of the real MO's and can be calculated much more easily and thus are very useful in analysis.

== Ammonia Borane ==

=== NH3 Optimization ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3.

<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>

NH3 log file - [[Media:JR_NH3_OPT.LOG|JR_NH3_OPT.LOG]]

[[File:NH3_optimization_Summary(jr1416).PNG]]

Frequency Analysis
<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)

=== NH3BH3 ===

The RB3LYP method and a basis set of 6-31G(d,p) was used to calculate and optimize the structure of NH3BH3.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

NH3BH3 log file - [[Media:JR_NH3BH3_OPT.LOG|JR_NH3BH3_OPT.LOG]]

[[File:NH3BH3_optimization_summary(jr1416).PNG]]

Frequency Analysis
<pre>
Low frequencies --- -0.0013 -0.0011 -0.0011 14.4660 22.7381 41.6444
Low frequencies --- 266.6526 632.2253 639.1944
</pre>

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_NH3BH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

=== NH3BH3 reaction Energies ===

E(NH3) = -56.5578 a.u. (-148490 kJmol-1)
E(BH3) = -26.6153 a.u. (-69880 kJmol-1)
E(NH3BH3) = -83.2247 a.u. (-218510 kJmol-1)

Er = E(NH3BH3)-(E(NH3)+E(BH3)) = -140 kJmol-1

This value for the association energy for ammonia borane is a sensible value as the energy of a C-N covalent bond is around -305 kJmol-1<ref>B═N Bond Cleavage and BN Ring Expansion at the Surface of Boron Nitride Nanotubes by Iminoborane
Rajashabala Sundaram, Steve Scheiner, Ajit K. Roy, and Tapas Kar
The Journal of Physical Chemistry C 2015 119 (6), 3253-3259
DOI: 10.1021/jp512753n</ref>. The bond energy of this dative bond is less due to the poorer overlap between B and N orbitals as compared to C and N. Compared to the C-N bond, the B-N bond is weak due to the poorer overlap integral.

== BBr3 ==

The B3LYP method and a basis set of 6-31G(d,p)LANL2DZ was used to calculate and optimize the structure of BBr3.

<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>

BBr3 log file - [[Media:JR_BBr3_OPT_3.log|JR_BBr3_OPT_3.log]]

[[File:JR_BBr3_Summary_table_2.PNG]]

Frequency Analysis
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052

<jmol><jmolApplet>
<title>optimised bromoborane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BBr3_OPT_3.log</uploadedFileContents>
</jmolApplet></jmol>

{{DOI|10042/202367}}

== Project section - Investigating Aromaticity ==

== Benzene ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000194 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000824 0.001800 YES
RMS Displacement 0.000289 0.001200 YES
</pre>

[[File:Benzene_Summary_table(jr1416).PNG]]

[[Media:JR_BENZENE_OPT.LOG|JR_BENZENE_OPT.LOG]]

Frequency Analaysis
Low frequencies --- -16.9682 -14.6636 -14.6636 -0.0055 -0.0055 -0.0005
Low frequencies --- 414.1239 414.1239 620.9400

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BENZENE_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Borazine ==

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000252 0.001800 YES
RMS Displacement 0.000075 0.001200 YES
</pre>

[[File:Borazine_Summary_Table(jr1416).PNG]]

[[Media:JR_BORAZINE_SYM_OPT.LOG|JR_BORAZINE_SYM_OPT.LOG]]

Frequency Analysis
Low frequencies --- -0.0013 -0.0012 -0.0012 3.4753 4.3539 6.8594
Low frequencies --- 289.7049 289.7804 404.4236

<jmol><jmolApplet>
<title>optimised borane molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>JR_BORAZINE_SYM_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Charge Analysis ==

{| class="wikitable"
|-
!
! Benzene Charge Analysis
! Borazine Charge Analysis
|-
| Colour Analysis
| [[File:Benzene_Charge_Analysis_Colour(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_Colour(jr1416).PNG|300px]]
|-
| Numerical Analysis
| [[File:Benzene_Charge_Analysis_No(jr1416).PNG|300px]]
| [[File:Borazine_Charge_Analysis_No(jr1416).PNG|300px]]
|}

== Molecular Orbital Analysis ==

{| class="wikitable"
|-
!
! Benzene MO
! Borazine MO
|-
| In phase s-orbital Bonding MOs
| [[File:Benzene_MO_1(jr1416).PNG|300px]]
|
|-
| π bonding MOs with 1 node
| [[File:Benzene_MO_2(jr1416).PNG|300px]]
|
|-
|
|
|
|-
|}

File:Benzene MO 2(jr1416).PNG

2018-05-10T12:36:41Z

Jr1416:

File:Benzene MO 1(jr1416).PNG

2018-05-10T12:30:26Z

Jr1416:

User:Molecular Modelling (jr1416)

2018-05-10T12:12:28Z

Jr1416: /* Charge Analysis */

File:Borazine Charge Analysis Colour(jr1416).PNG

2018-05-10T12:12:08Z

Jr1416: Jr1416 uploaded a new version of File:Borazine Charge Analysis Colour(jr1416).PNG